{"id":3155,"date":"2023-12-18T14:22:05","date_gmt":"2023-12-18T08:52:05","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=3155"},"modified":"2023-12-19T10:09:41","modified_gmt":"2023-12-19T04:39:41","slug":"envision-math-common-core-grade-7-answer-key-topic-7","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-7-answer-key-topic-7\/","title":{"rendered":"enVision Math Common Core Grade 7 Answer Key Topic 7 Probability"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 7 Answer Key<\/a>\u00a0Topic 7 Probability<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 7th Grade Answers Key Topic 7 Probability<\/h2>\n

GET READY!
\nReview What You Know!<\/strong><\/p>\n

Vocabulary<\/strong>
\nChoose the best term from the box to complete each definition.
\n\"Envision<\/p>\n

Question 1.
\nA(n) _________ is a drawing that can be used to visually represent information.<\/p>\n

Answer:
\nA(n) diagram is a drawing that can be used to visually represent information.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA(n) diagram is a drawing that can be used to visually represent information.
\nfor example:
\na diagram is a visual representation of information.
\ndiagrams can be both two-dimensional and three-dimensional.
\nsome of the most common types of diagrams are flowcharts.<\/p>\n

Question 2.
\nThe number of times a specific value occurs is referred to as _________.<\/p>\n

Answer:
\nThe number of times a specific value occurs is referred to as frequency.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number of times a specific value occurs is referred to as frequency.
\nfor example:
\n3, 3, 5, 5, 5, 6, 7, 7, 7, 7, and 7.
\nfrom the above data set – 3 occurs 2 times, then 2 is the frequency of 3.
\n5 occurs 3 times, then 3 is the frequency of 5.
\n6 occurs 1 time, then 1 is the frequency of 6.<\/p>\n

Question 3.
\nA(n) _________ is a relationship between one quantity and another quantity.<\/p>\n

Answer:
\nA(n) ratio is a relationship between one quantity and another quantity.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA(n) ratio is a relationship between one quantity and another quantity.
\nfor example:
\nthere are 3 boys and 6 girls in a class.
\ntherefore the ratio is 1: 2.<\/p>\n

Question 4.
\nQuantities that have the same value are<\/p>\n

Answer:
\nQuantities that have the same value are equivalent ratios.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nQuantities that have the same value are equivalent ratios.
\nfor example:
\nthe cost of the order is 8.
\npizzas ordered is 1.
\n8\/1 = 16\/2 = 24\/3 = 32\/4 = 40\/5 = 8.
\nso $8 per pizza.<\/p>\n

Operations with Fractions
\nSolve for x.<\/p>\n

\"Math<\/p>\n

Question 5.
\n\\(\\frac{2}{5}\\) + x = 1<\/p>\n

Answer:
\n2\/5 + x = 1 is 0.6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n\\(\\frac{2}{5}\\) + x = 1.
\n2\/5 + x = 1.
\n0.4 + x = 1.
\nx = 1 – 0.4.
\nx = 0.6.
\nso the value of x is 0.6.<\/p>\n

Question 6.
\n225 \u2022 \\(\\frac{1}{3}\\)= x<\/p>\n

Answer:
\n225 (1\/3) = x is 75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n225 \u2022 \\(\\frac{1}{3}\\)= x
\n225(1\/3) = x.
\n75 = x.
\nso the value of x is 75.<\/p>\n

Question 7.
\n1 = \\(\\frac{1}{8}\\) + x + \\(\\frac{2}{8}\\)<\/p>\n

Answer:
\n1 = 1\/8 + x + 2\/8 is 0.625.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n1 = \\(\\frac{1}{8}\\) + x + \\(\\frac{2}{8}\\).
\n1 = 0.125 + x + 0.25.
\n1 – 0.125 = x + 0.25.
\n0.875 – 0.25 = x.
\nx = 0.625.
\nso the value of x is 0.625.<\/p>\n

Ratios<\/strong>
\nWrite each ratio in fraction form. Then write the percent equivalent.<\/p>\n

Question 8.
\n72 out of 96<\/p>\n

Answer:
\n72\/96 = 0.75.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n72 out of 96.
\n72\/96.
\n0.75.<\/p>\n

Question 9.
\n88 out of 132<\/p>\n

Answer:
\n88\/132 = 0.66.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n88 out of 132.
\n88\/132.
\n0.66.<\/p>\n

\"Math<\/p>\n

Question 10.
\n39 out of 104<\/p>\n

Answer:
\n39\/104 = 0.375.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n39 out of 104.
\n39\/104.
\n0.375.<\/p>\n

Question 11.
\n23 out of 69<\/p>\n

Answer:
\n23\/69 = 0.33.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n23 out of 69.
\n23\/69.
\n0.33.<\/p>\n

Question 12.
\n52 out of 208<\/p>\n

Answer:
\n52\/208 = 0.25.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n52 out of 208.
\n52\/208.
\n0.25.<\/p>\n

Question 13.
\n25 out of 200<\/p>\n

Answer:
\n25\/200 = 0.125.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n25 out of 200.
\n25\/200.
\n0.125.<\/p>\n

Order Fractions and Decimals<\/strong>
\nPlot the following fractions and decimals on the number line.
\n\"Envision<\/p>\n

Answer:
\nThe fractions and decimals are 0.7, 1\/3, 7\/8, 0.4, 0.125, and 5\/6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe fractions and decimals are 0.7, 1\/3, 7\/8, 0.4, 0.125, and 5\/6.
\n1\/3 = 0.3.
\n7\/8 = 0.875.
\n5\/6 = 0.83.
\n1\/4 = 0.25.
\n1\/2 = 0.5.
\n3\/4 = 0.75.
\n0.7 lies in between 3\/4 and 1.
\n0.3 lies in between 1\/4 and 1\/2.
\n7\/8 lies in between 3\/4 and 1.
\n0.4 lies in between 1\/4 and 1\/2.
\n5\/6 lies in between 3\/4 and 1.
\n0.125 lies in between 0 and 1\/4.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-1\"<\/p>\n

Language Development<\/strong>
\nSort the vocabulary words into categories. Explain your categories.
\n\"Envision<\/p>\n

Category: Probability.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nprobability of a given event is an expression of the likelihood of occurrence of an event.
\na probability is a number that ranges from 0 to 1.
\nthere are so many types of probabilities are there.
\nthey are theoretical probability and experimental probability.
\nfor example:
\n0 for an event that cannot occur.
\n1 for an event that can occur.<\/p>\n

Category: Event.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nan event is a subject of the sample space.
\nthat is any collection of outcomes from an event.
\nevents will be denoted b capital letters.<\/p>\n

Category: Frequency.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nfrequency is the rate at which something occurs over a particular period of time or in a given sample.
\nsample space and relative frequency come under this.
\nfor example:
\n3, 3, 5, 5, 5, 6, 7, 7, 7, 7, and 7.
\nfrom the above data set – 3 occurs 2 times, then 2 is the frequency of 3.
\n5 occurs 3 times, then 3 is the frequency of 5.
\n6 occurs 1 time, then 1 is the frequency of 6.<\/p>\n

Category: Simulation.<\/p>\n

Pick A Project<\/strong><\/p>\n

PROJECT 7A<\/strong>
\nWhat makes a carnival game fun and successful?<\/p>\n

PROJECT: DEVELOP A GAME OF CHANCE<\/strong><\/p>\n

PROJECT 7B<\/strong>
\nIf you could invent a character for an adventure, what would that character be like?
\nProject: Design An Adventure<\/p>\n

PROJECT 7C<\/strong>
\nWhat is the silliest sentence you can think of? Why is it silly?
\nProject: Generate A Funny Sentence<\/p>\n

PROJECT 7D<\/strong>
\nHow could you teach a math concept through a performance?
\nProject: Perform Your Knowledge<\/p>\n

Lesson 7.1 Understand Likelihood and Probability<\/h3>\n

Solve & Discuss It!<\/strong>
\nFor a game show, Jared has to choose 1 of 8 boxes to win a prize. One of the boxes has a big prize, 3 boxes have a medium prize, 3 boxes have smaller prizes, and 1 box is empty. How confident should Jared be that whatever box he chooses, he will win a prize? Support your response with a mathematical argument.
\nI can… describe the likelihood that an event will occur.
\n\"Envision<\/p>\n

Make Sense and Persevere<\/strong>
\nWhat are the chances that Jared will choose a box with a prize?<\/p>\n

Answer:
\nThe three chances are 3\/8, 1\/8, and 3\/8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJared has to choose 1 of 8 boxes to win a prize.
\nOne of the boxes has a big prize, 3 boxes have a medium prize, 3 boxes have smaller prizes, and 1 box is empty.
\n1 out of 8 boxes is 1\/8.
\n3 out of 8 is 3\/8 medium prize.
\n3\/8 smaller prize.
\n1 box is empty is 1\/8.
\nthere are 3 chances.
\nthey are 3\/8, 1\/8, and 3\/8.<\/p>\n

\"Math<\/p>\n

Focus on math practices<\/strong>
\nConstruct Arguments Suppose the empty box is taken out of the game.
\nHow confident should Jared be that he will win a prize? Explain.<\/p>\n

Essential Question<\/strong> what is probability?<\/p>\n

Try It!<\/strong>
\nHow might the probability of the pointer landing on a given color change for the spinner shown at the right?<\/p>\n

Convince Me!<\/strong> How would the probability of the pointer landing on a given color change if the spinner had six equal-sized sections with each section a different color?<\/p>\n

Try It!<\/strong>
\nThe game piece shown has 12 sides, labeled 1 to 12.
\n\"Envision<\/p>\n

a. What is the probability of rolling an 11?<\/p>\n

Answer:
\nThe probability of rolling an 11 is 11\/12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe game piece shown has 12 sides, labeled 1 to 12.
\nthe probability of rolling an 11 is 11\/12.
\nso the event is on 11\/12.<\/p>\n

b. What is the probability of rolling a number greater than 5?<\/p>\n

Answer:
\nThe probability of rolling a number greater than 5 is 7\/12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe game piece shown has 12 sides, labeled 1 to 12.
\nthe probability of rolling a number greater than 5 in 12 – 7.
\n12 – 7 = 5.
\nso the probability of rolling a number greater than 5 is 7\/12.<\/p>\n

c. What is the probability of rolling a number greater than 12?<\/p>\n

Answer:
\nThe probability of rolling a number greater than 12 is 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe game piece shown has 12 sides, labeled 1 to 12.
\n12\/12 = 1.
\nso the probability of rolling a number greater than 12 is 1.<\/p>\n

Try It!<\/strong>
\nIs the spinner shown a fair spinner? If yes, explain why. If not, describe a change that could make the spinner fair.
\n\"Envision<\/p>\n

Answer:
\nYes, the spinner is not a fair spinner.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe fair spinner is on the 12 hands.
\n12\/6 = 2.
\nso the spinner is not a fair spinner.<\/p>\n

KEY CONCEPT<\/strong>
\nThe probability that something will occur is a value from 0 to 1, which describes its likelihood. You can write probability as a ratio, such as 1 out of 2, or 3, or as a percent, such as 50%.
\n\"Envision<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question What is probability?<\/p>\n

Answer:
\nThe probability of a given event is an expression of the likelihood of occurrence of an event.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nprobability of a given event is an expression of the likelihood of occurrence of an event.
\na probability is a number that ranges from 0 to 1.
\nthere are so many types of probabilities are there.
\nthey are theoretical probability and experimental probability.
\nfor example:
\n0 for an event that cannot occur.
\n1 for an event that can occur.<\/p>\n

Question 2.
\nConstruct Arguments How can you use probability to draw conclusions about the likelihood that something will occur?<\/p>\n

Answer:
\n0 for an event that cannot occur.
\n1 for an event that can occur.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nprobability of a given event is an expression of the likelihood of occurrence of an event.
\na probability is a number that ranges from 0 to 1.
\nthere are so many types of probabilities are there.
\nthey are theoretical probability and experimental probability.
\nfor example:
\n0 for an event that cannot occur.
\n1 for an event that can occur.<\/p>\n

Question 3.
\nReasoning Why is probability limited to numbers between 0 and 1?<\/p>\n

Answer:
\nThe probability limited to numbers between 0 and 1 is 0.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nprobability of a given event is an expression of the likelihood of occurrence of an event.
\na probability is a number that ranges from 0 to 1.
\nthere are so many types of probabilities are there.
\nthey are theoretical probability and experimental probability.
\nfor example:
\n0 for an event that cannot occur.
\n1 for an event that can occur.<\/p>\n

\"Math<\/p>\n

Do You Know How?<\/strong>
\nAllie is going to select a card from the group of cards shown. Complete each statement.
\n\"Envision<\/p>\n

Question 4.
\nThe probability that Allie will select a card labeled 3 is _________ out of 10, or _________%.<\/p>\n

Answer:
\nThe probability that Allie will select a card labeled 3 is 2 out of 10, or 0.002.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAllie is going to select a card from the group of cards shown.
\n3 is 2 out of 10.
\n3 is 2\/10.
\n3 is 1\/5 = 0.2.<\/p>\n

Question 5.
\nBecause the probability that each number will be selected is not _________, the group of cards is not fair.<\/p>\n

Answer:
\nBecause the probability that each number will be selected is not fair, the group of cards is not fair.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAllie is going to select a card from the group of cards shown.
\n5 out of 10 is 5\/10 = 1\/2.
\nso the probability that each number will be selected is not fair.<\/p>\n

Question 6.
\nIt is _________ that Allie will select a card labeled with a number less than 6.<\/p>\n

Answer:
\n5\/10 = 1\/2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAllie is going to select a card from the group of cards shown.
\nIt is 5 that Allie will select a card labeled with a number less than 6.
\n5\/10 = 1\/2.<\/p>\n

Question 7.
\nIt is _________ that Allie will select a card labeled 4.<\/p>\n

Answer:
\nIt is 4\/10 that Allie will select a card labeled 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAllie is going to select a card from the group of cards shown
\nit is 4\/10 that Allie will select a card labeled 4.
\n4\/10 = 2\/5.
\n2\/5 = 0.4.<\/p>\n

Practice & Problem Solving<\/strong><\/p>\n

Leveled Practice In 8-10, fill in the boxes to complete each statement.<\/p>\n

Question 8.
\nA spinner has 8 equal-sized sections. Six of the sections are green.<\/p>\n

Answer:
\n6 out of 8 sections are green.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA spinner has 8 equal-sized sections. Six of the sections are green.
\n6\/8 = 3\/4.
\n6 out of 8 sections are green.
\n3\/4 = 0.75.<\/p>\n

a. What is the probability that the spinner will land on green?
\n\"Envision<\/p>\n

Answer:
\nThe missing numbers are 6, 3, and 75%.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n6 out of 8.
\n6\/8 = 3\/4.
\n3\/4 = 0.75.
\n0.75\/100 = 75.
\nso the missing numbers are 6, 3, and 75%.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-2\"<\/p>\n

b. Use words to describe the probability.
\nIt is _________ that the spinner will land on green.<\/p>\n

Answer:
\nIt is 6 out of 8 that the spinner will land on the green.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n6 out of 8.
\n6\/8 = 3\/4.
\n3\/4 = 0.75.<\/p>\n

Question 9.
\nMarcus is rolling a number cube with sides labeled 1 to 6.
\na. The probability that the number cube will _________ show 10 is _________.<\/p>\n

Answer:<\/p>\n

b. It is _________ that the number cube will show 10.
\nAnswer:<\/p>\n

Question 10.
\nOf the marbles in a bag, 3 are yellow, 2 are red, and 2 are blue. Sandra will randomly choose one marble from the bag.
\na. The probability that Sandra will choose a blue marble from the bag is _________ out of _________, or _________.<\/p>\n

Answer:
\nThe probability that Sandra will choose a blue marble from the bag is 1 out of 7 marbles or 1\/7.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOf the marbles in a bag, 3 are yellow, 2 are red, and 2 are blue.
\nSandra will randomly choose one marble from the bag.
\n3 + 2 + 2 = 7.
\n1 out of 7.
\n1\/7 is 0.142.<\/p>\n

b. It is _________ that sandra will choose a blue marble from the bag.<\/p>\n

Answer:
\nIt is 1\/7 that Sandra will choose a blue marble from the bag.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOf the marbles in a bag, 3 are yellow, 2 are red, and 2 are blue.
\nSandra will randomly choose one marble from the bag.
\n3 + 2 + 2 = 7.
\n1 out of 7.
\n1\/7.<\/p>\n

Question 11.
\nSuppose you have a bag with 20 letter tiles in it, and 3 of the tiles are labeled Y. Suppose a second bag has 500 letter tiles in it, and 170 of the tiles are labeled Y. From which bag are you more likely to pick a tile that is labeled Y? Explain.
\n\"Envision<\/p>\n

Answer:
\nWe will choose the bag with 20 letter tiles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nyou have a bag with 20 letter tiles in it, and 3 of the tiles are labeled Y.
\n20\/3 = 6.6.
\nSuppose a second bag has 500 letter tiles in it, and 170 of the tiles are labeled Y.
\n500\/170 = 2.9.
\nso we will choose the bag with 20 letter tiles.<\/p>\n

\"Math<\/p>\n

Question 12.
\nMake Sense and Persevere Suppose you have a bag of 40 marbles, and 20 of them are white. If you choose a marble without looking, the probability that you choose a white marble is \\(\\frac{20}{40}\\). Describe the probability.<\/p>\n

Answer:
\nThe probability is 20\/40 is 0.5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nyou have a bag of 40 marbles, and 20 of them are white.
\nIf you choose a marble without looking, the probability that you choose a white marble is \\(\\frac{20}{40}\\).
\n20\/40 = 1\/2.
\n1\/2 = 0.5.<\/p>\n

Question 13.
\nSuppose Nigel has a bag of colored wristbands, and he chooses one without looking. The bag contains a total of 25 wristbands and 6 of the wristbands are blue.
\n\"Envision<\/p>\n

Answer:
\n1 out of 25 = 0.04.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nNigel has a bag of colored wristbands, and he chooses one without looking.
\nThe bag contains a total of 25 wristbands and 6 of the wristbands are blue.
\n1 out of 25.
\n1\/25.<\/p>\n

a. What is the probability that Nigel will choose a blue wristband?<\/p>\n

Answer:
\nThe probability is 6\/25.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nNigel has a bag of colored wristbands, and he chooses one without looking.
\nThe bag contains a total of 25 wristbands and 6 of the wristbands are blue.
\n6 out of 25.
\n6\/25.
\nso the probability that Nigel will choose a blue wristband.<\/p>\n

b. Is it likely, unlikely, or neither likely nor unlikely that Nigel will choose a blue wristband?<\/p>\n

Answer:
\nIt is neither likely nor unlikely that Nigel will choose a blue wristband.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nNigel has a bag of colored wristbands, and he chooses one without looking.
\nThe bag contains a total of 25 wristbands and 6 of the wristbands are blue.
\n6 out of 25.
\n6\/25.<\/p>\n

Question 14.
\nA box contains four equal-sized cards labeled 1, 3, 5, and 7. Tim will select one card from the box.
\na. What is the probability that Tim will select a card labeled 4?<\/p>\n

Answer:
\nThe probability that Tim will select a card labeled 4 is 1\/4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA box contains four equal-sized cards labeled 1, 3, 5, and 7.
\n1, 3, 5, and 7.
\n4 out of 16.
\n4\/16 = 1\/4.<\/p>\n

b. What is the probability that Tim will select a card labeled with a number less than 6?<\/p>\n

Answer:
\nThe probability that Tim will select a card labeled with a number less than 6 is 5\/16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe probability that Tim will select a card labeled with a number less than 6.
\n5 out of 16.
\n5\/16.
\n0.3125.<\/p>\n

c. What is the probability that Tim will select a card labeled with an odd number?<\/p>\n

Answer:
\nThe probability that Tim will select a card labeled with an odd number is 5\/16.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe probability that Tim will select a card labeled with an odd number.
\n5 out of 16.
\n5\/16.
\n0.3125.<\/p>\n

Question 15.
\nModel with Math<\/strong> Henry is going to color a spinner with 10 equal-sized sections. Three of the sections will be orange and 7 of the sections will be purple. Is this spinner fair? If so, explain why. If not, explain how to make it a fair spinner.<\/p>\n

Answer:
\nYes, It is fair.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nHenry is going to color a spinner with 10 equal-sized sections.
\nThree of the sections will be orange and 7 of the sections will be purple.
\n3\/10 and 7\/10.
\n3 out of 10.
\n7 out of 10.
\n7 + 3 = 10.
\nso it is fair.<\/p>\n

Question 16.
\nHigher Order Thinking<\/strong> Without being able to calculate probability, describe the likelihood that the following event will occur.
\nAll 21 students in a class share the same birthday.<\/p>\n

Answer:
\nThe probability is 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nWithout being able to calculate probability,
\ndescribe the likelihood that the following event will occur.
\nAll 21 students in a class share the same birthday.
\n21\/ 21 = 1.
\nit is the like event.<\/p>\n

Assessment Practice<\/strong>
\nQuestion 17.
\nAfter many studies, a researcher finds that the probability that a word recognition app correctly interprets a handwritten word is \\(\\frac{9}{10}\\). Which statement is true?
\nA It is impossible that the handwritten word will be correctly interpreted.
\nB It is unlikely that the handwritten word will be correctly interpreted.
\nC It is likely that the handwritten word will be correctly interpreted.
\nD It is certain that the handwritten word will be correctly interpreted.<\/p>\n

Answer:
\nOption A is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAfter many studies, a researcher finds that the probability that a word recognition app correctly interprets a handwritten word is 9\/10.
\n9 out of 10 words.
\n9\/10.
\nit is impossible that the handwritten word will be correctly interpreted.
\nso option A is correct.<\/p>\n

Question 18.
\nA bag contains 8 letter tiles of the same size. The tiles are labeled either A, B, C, D, E, or F. Three of the tiles are labeled C. If Corey selects 1 tile from the bag without looking, is the selection of letters fair? Explain.<\/p>\n

Answer:
\nYes, the selection of letters is fair.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA bag contains 8 letter tiles of the same size.
\nThe tiles are labeled either A, B, C, D, E, or F.
\nThree of the tiles are labeled C.
\n1 out of 8.
\n1\/8.
\nso the selection of letters is fair.<\/p>\n

Lesson 7.2 Understand Theoretical Probability<\/p>\n

Solve & Discuss It!<\/strong><\/p>\n

Betty and Carl will conduct an experiment. They will flip a coin 100 times and record the result of each flip. What should they expect the results of their experiment to be? Justify your answer.
\n\"Envision
\nI can… determine the theoretical probability of an event.<\/p>\n

Answer:
\nThe theoretical probability of an event is 1\/100, 2\/100, ….. 100\/100.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBetty and Carl will conduct an experiment.
\nThey will flip a coin 100 times and record the result of each flip.
\nso the theoretical probability of an event is,
\n1\/100, 2\/100, .. 50\/100, …. 100\/100.<\/p>\n

Focus on math practices<\/strong>
\nLook for Relationships How would their expected results change if Betty and Carl flipped a coin 500 times?<\/p>\n

Essential Question<\/strong>
\nHow can the probability of an event help make predictions?<\/p>\n

Try It!<\/strong>
\nIf Talia and Yoshi redesign their spinner to have 14 sections instead of 16 sections, would they likely have more or fewer winners? Explain why.
\n\"Envision<\/p>\n

Answer:
\nThey have fewer winners.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf Talia and Yoshi redesign their spinner to have 14 sections instead of 16 sections.
\n14\/2 = 7.
\n16\/2 = 8.
\nso they have fewer winners.<\/p>\n

Convince Me!<\/strong> If there are always 2 red sections, how does the number of total sections in the spinner relate to the theoretical probability of winning this game?<\/p>\n

Answer:
\nThe probability of winning this game is 2 out of 14.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf there are always 2 red sections, how does the number of total sections in the spinner relate to the theoretical probability of winning this game?
\n2\/14 = 1\/7.
\nso the probability of the game is 2\/14.<\/p>\n

Try It!<\/strong>
\nJoaquin wants to reduce the number of winners so he does not have to prepare as many prizes. Choose another sum he could use as a winning sum, and predict the number of winners if 500 people play his game.<\/p>\n

Answer:
\nThe number of winners is 10.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJoaquin wants to reduce the number of winners so he does not have to prepare as many prizes.
\n500\/50 = 10.
\nso the number of winners is 10.<\/p>\n

KEY CONCEPT<\/strong>
\nYou can determine the theoretical probability of an event, Plevent), if you know all the possible outcomes and they are equally likely.
\n+ number of favorable outcomes
\n\"Envision<\/p>\n

You can use theoretical probability and proportional reasoning to make predictions, such as in a game situation.
\n\"Envision<\/p>\n

Do You Understand?<\/strong><\/p>\n

Question 1.
\nEssential Question<\/strong> How can the probability of an event help make predictions?<\/p>\n

Answer:
\nThe number of favorable outcomes\/ total number of possible outcomes is equal to the number of winning outcomes\/ total number of possible outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe probability of an event help make predictions are:
\nthe number of favorable outcomes\/ total number of possible outcomes is equal to the number of winning outcomes\/ total number of possible outcomes.<\/p>\n

Question 2.
\nConstruct Arguments<\/strong> A game board has a spinner with 10 equal-sized sections, of which 4 are green, 3 are blue, 2 are yellow, and 1 is red. What is the sum of the probabilities of the pointer landing in the green, blue, yellow, and red sections? Explain.<\/p>\n

Answer:
\np(event) = 1\/5.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA game board has a spinner with 10 equal-sized sections, of which 4 are green, 3 are blue, 2 are yellow, and 1 is red.
\nthe sum of the probabilities of the pointer landing in the green, blue, yellow, and red.
\np(event) = number of favorable outcomes\/total number of possible outcomes.
\np(event) = 4 \/ 10 + 4 + 3 + 2 + 1.
\np(event) = 4\/20.
\np(event) = 1\/5.<\/p>\n

Question 3.
\nReasoning<\/strong> What does it mean that there is an equal theoretical probability of each outcome? Explain.<\/p>\n

Answer:
\nThe theoretical probability of each outcome = number of favorable outcomes\/ total number of possible outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe probability of an event help make predictions are:
\nthe number of favorable outcomes\/ total number of possible outcomes is equal to the number of winning outcomes\/ total number of possible outcomes.<\/p>\n

Do You Know How?<\/strong>
\nIn 4-6, Monique rolls a six-sided number cube labeled 1 to 6.<\/p>\n

Question 4.
\nFind P(rolling a 4).<\/p>\n

Answer:
\np(rolling a 4) = 4\/6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMonique rolls a six-sided number cube labeled 1 to 6.
\np(rolling a 4) = number of favorable outcomes\/ total number of possible outcomes.
\np(rolling a 4) = 4\/6.<\/p>\n

Question 5.
\nFind P(rolling an odd number).<\/p>\n

Answer:
\np(rolling an odd number) = 3\/6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMonique rolls a six-sided number cube labeled 1 to 6.
\np(rolling an odd number) = number of favorable outcomes\/ total number of possible outcomes.
\np(rolling an odd number) = 3\/6.<\/p>\n

Question 6.
\nIf Monique rolls the number cube 12 times, how many times would she expect a number greater than 4 to be rolled?<\/p>\n

Answer:
\nThe number of times would she expect a number greater than 4 to be rolled = 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIf Monique rolls the number cube 12 times.
\np(event) = 4\/12.
\np(event) = 1\/3.
\nso the number of times would she expect a number greater than 4 to be rolled = 3.<\/p>\n

Practice & Problem Solving<\/strong>
\nLeveled Practice<\/strong> In 7-9, complete each statement.<\/p>\n

Question 7.
\nA spinner has 8 equal-sized sections. To win the game, the pointer must land on a yellow section.
\n\"Envision<\/p>\n

Answer:
\nP(yellow) = 2\/8 = 1\/4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA spinner has 8 equal-sized sections.
\n2\/8 = 1\/4.
\nso to win the game the pointer must land on a yellow section is 1\/4.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-3\"<\/p>\n

Question 8.
\nNatalie is playing a game using a fair coin. Contestants win the game if the fair coin lands tails up.
\nThe theoretical probability that the coin will land tails up is _________.
\nIf 250 contestants play the game, about of them are expected to win.<\/p>\n

Answer:
\n250\/250 = 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nNatalie is playing a game using a fair coin.
\nContestants win the game if the fair coin lands tail up.
\nIf 250 contestants play the game, about of them are expected to win.
\nso the theoretical probability = 1.<\/p>\n

Question 9.
\nIn a different game, the probability of correctly guessing which of 5 boxes contains a tennis ball is \\(\\frac{1}{5}\\). About how many winners would be expected if 60 contestants play the game?
\n\"Envision
\nX = _________ winners<\/p>\n

Answer:
\nThe number of winners would be expected if 60 contestants play the game = 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe probability of correctly guessing which of 5 boxes contains a tennis ball is 1\/5.
\n1\/5 = x\/60.
\nx = 1\/5 x 60.
\nx = 12.
\nso the number of winners would be expected if 60 contestants play the game = 12.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-4\"<\/p>\n

Question 10.
\nMake Sense and Persevere<\/strong> A 12-sided solid has equal-sized faces numbered 1 to 12.
\na. Find P(number greater than 10).
\nb. Find P(number less than 5).
\nc. If the 12-sided solid is rolled 200 times, how many times would you expect either a 4, 6, or 9 to be rolled?
\n\"Envision<\/p>\n

Answer:
\na. p (number gteater than 10) = 10\/12.
\nb. p(number less than 5) = 5\/12.
\nc. 12-sided solid is rolled 200 times = 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA 12-sided solid has equal-sized faces numbered 1 to 12.
\na. p (number gteater than 10) = 10\/12.
\nb. p(number less than 5) = 5\/12.
\nc. 12-sided solid is rolled 200 times = 6.<\/p>\n

Question 11.
\nTamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
\n\"Envision<\/p>\n

Answer:
\nThe number of times should Tamara expect the sum of the two cubes to be equal to 5 is 36 times.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTamara finds the sum of two number cubes rolled at the same time.
\nThe chart below shows all possible sums from the 36 possible combinations when rolling two number cubes.
\n180\/5 = 36.
\nso the number of times should Tamara expect the sum of the two cubes to be equal to 5 is 36 times.<\/p>\n

Question 12.
\nHigher Order Thinking<\/strong> A store is giving every customer who enters the store a scratch-off card labeled with numbers from 1 to 10. It is equally likely that any of the numbers from 1 to 10 will be labeled on a given card. If the card is an even number, the customer gets a 15% discount on a purchase. If the card is an odd number greater than 6, the customer gets a 30% discount. Otherwise, the discount is 20%.
\n\"Envision<\/p>\n

a. What is the probability for each discount?
\n15% discount: _________
\n20% discount: _________
\n30% discount: _________<\/p>\n

Answer:
\nA card is an even number the customer gets a 15% discount.
\nif the card is an odd number greater than 6 the customer gets a 30% discount.
\na card is an odd number the customer gets a 20% discount.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA store is giving every customer who enters the store a scratch-off card labeled with numbers from 1 to 10.
\nIt is equally likely that any of the numbers from 1 to 10 will be labeled on a given card.
\nIf the card is an even number, the customer gets a 15% discount on a purchase.
\nA card is an even number the customer gets a 15% discount.
\nif the card is an odd number greater than 6 the customer gets a 30% discount.
\na card is an odd number the customer gets a 20% discount.<\/p>\n

b. The store manager gives out 300 scratch-off cards. Which discount will the greatest number of customers likely receive? Explain.<\/p>\n

Answer:
\nThe greatest number of customers likely receive is 3%.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe store manager gives out 300 scratch-off cards.
\n300\/100 = 3.
\nso the greatest number of customers likely receive is 3%.<\/p>\n

Assessment Practice<\/strong><\/p>\n

Question 13.
\nA spinner is divided into 4 equal parts. 1 part is colored red, 2 parts are colored blue, and 1 part is colored yellow. The spinner is spun 1,000 times. Select all of the reasonable possible outcomes.
\n\u2610 The spinner lands on blue 445 times.
\n\u2610 The spinner lands on red 430 times.
\n\u2610 The spinner lands on blue 290 times.
\n\u2610 The spinner lands on yellow 200 times.
\n\u2610 The spinner lands on red 290 times.<\/p>\n

Answer:
\nThe spinner lands on blue 445 times.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA spinner is divided into 4 equal parts.
\n1 part is colored red, 2 parts are colored blue, and 1 part is colored yellow.
\nThe spinner is spun 1,000 times.
\n1000\/2 = 500.
\nso the spinner lands on blue 445 times.<\/p>\n

Question 14.
\nOne thousand five hundred runners have signed up for a marathon. The probability of a runner finishing the race is \\(\\frac{11}{12}\\). Approximately how many runners are expected to finish the race?<\/p>\n

Answer:
\nThe number of runners is expected to finish the race = 125.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne thousand five hundred runners have signed up for a marathon.
\nThe probability of a runner finishing the race is \\(\\frac{11}{12}\\).
\n11\/12 = 0.916.
\n1500 \/ 12 = 125.
\nso the number of runners are expected to finish the race = 125.<\/p>\n

Lesson 7.3 Understand Experimental Probability<\/h3>\n

Solve & Discuss It!<\/strong>
\nKevin is awarded a penalty shot. He will either score a goal or not score a goal. Are both outcomes equally likely? Explain.
\n\"Envision
\nI can… determine the experimental probability of an event.<\/p>\n

Look for Relationships
\nWhat might affect the outcome?<\/p>\n

Answer:
\nYes, both outcomes are equally likely.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nKevin is awarded a penalty shot.
\nHe will either score a goal or not score a goal.
\nso both outcomes are equally likely.<\/p>\n

Focus on math practices
\nConstruct Arguments Lowe Senior High School’s soccer team won 12, lost 5, and tied in 3 of their first 20 games this season. Which outcome is most likely for the team’s next game? Explain your reasoning.
\n\"Envision<\/p>\n

Answer:
\nThe outcome is most likely for the team’s next game is 0.15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLowe Senior High School’s soccer team won 12, lost 5, and tied in 3 of their first 20 games this season.
\n12\/5 = 122.6.
\n3\/20 = 0.15.
\nso the outcome is most likely for the team’s next game is 0.15.<\/p>\n

Essential Question<\/strong>
\nHow is experimental probability similar to and different from theoretical probability?<\/p>\n

Try It!<\/strong><\/p>\n

During the second day of the school fair, Talia and Yoshi recorded 43 winners out of a total of 324 players. How does the actual number of winners compare to the expected number of winners?
\nTheoretical Probability
\nP(red) = \\(\\frac{1}{8}\\) = 12.5%<\/p>\n

Experimental Probability
\n\\(\\frac{1}{324}\\) \u2248 ________ %
\nThis experimental probability is ________ than the theoretical probability.
\nThere were ________ winners than expected.<\/p>\n

Convince Me!<\/strong> Will experimental probability always be close to theoretical probability? Explain.<\/p>\n

Try It!<\/strong><\/p>\n

Amir and Marvin continue until they each flip a coin 200 times. How do you expect Amir’s results and Marvin’s results to compare? How will their results compare with expected results based on theoretical probability?<\/p>\n

Answer:
\nThe expected results are based on theoretical probability = 100.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAmir and Marvin continue until they each flip a coin 200 times.
\n200\/2 = 100.
\nso the expected results are based on theoretical probability = 100.<\/p>\n

KEY CONCEPT<\/strong>
\nRelative frequency, or experimental probability, is based on the actual results of an experiment, while theoretical probability is based on calculated results from the knowledge of the possible outcomes. Experimental probability and theoretical probability may be close but are rarely exactly the same.
\n\"Envision
\nThe experimental probability tends to get closer to the theoretical probability of an experiment as more trials are conducted.<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question<\/strong> How is experimental probability similar to and different from theoretical probability?<\/p>\n

Answer:
\nThe number of times an event occurs \/ total number of times the experiment is carried out.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRelative frequency, or experimental probability, is based on the actual results of an experiment,
\nwhile theoretical probability is based on calculated results from the knowledge of the possible outcomes.
\nExperimental probability = number of times an event occurs\/ total number of times the experiment is carried out.
\nthis value changes each time an experiment is carried out.<\/p>\n

Question 2.
\nConstruct Arguments<\/strong> How can experimental probability be used to make predictions?<\/p>\n

Answer:
\nThe number of times an event occurs \/ total number of times the experiment is carried out.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRelative frequency, or experimental probability, is based on the actual results of an experiment,
\nwhile theoretical probability is based on calculated results from the knowledge of the possible outcomes.
\nExperimental probability = number of times an event occurs\/ total number of times the experiment is carried out.
\nthis value changes each time an experiment is carried out.<\/p>\n

Question 3.
\nReasoning<\/strong> is experimental probability always close to theoretical probability? Explain.<\/p>\n

Answer:
\nThe number of times an event occurs \/ total number of times the experiment is carried out.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRelative frequency, or experimental probability, is based on the actual results of an experiment,
\nwhile theoretical probability is based on calculated results from the knowledge of the possible outcomes.
\nExperimental probability = number of times an event occurs\/ total number of times the experiment is carried out.
\nthis value changes each time an experiment is carried out.<\/p>\n

Do You Know How?<\/strong>
\nIn 4\u20136, complete each statement. Kelly flips a coin 20 times. The results are shown in the table, where “H” represents the coin landing heads up and “T” represents the coin landing tails up.
\n\"Envision<\/p>\n

Question 4.
\nThe theoretical probability that the coin will land heads up is _________.<\/p>\n

Answer:
\nThe theoretical probability that the coin will land heads up is 9\/20 times.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nKelly flips a coin 20 times.
\nthe results were shown in the table.
\nT represents the coin landing tails up.
\nso the theoretical probability that the coin will land heads up is 9\/20 times.<\/p>\n

Question 5.
\nBased on the data, the experimental probability that the coin will land heads up is __________.<\/p>\n

Answer:
\nThe experimental probability that the coin will land heads up is 11\/20 times.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nKelly flips a coin 20 times.
\nthe results were shown in the table.
\nH represents the coin landing the heads up.
\nso the experimental probability that the coin will land heads up is 11\/20 times.<\/p>\n

Question 6.
\nThe experimental probability is _________ than the theoretical probability.<\/p>\n

Answer:
\nThe experimental probability is greater than the theoretical probability.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRelative frequency, or experimental probability, is based on the actual results of an experiment,
\nwhile theoretical probability is based on calculated results from the knowledge of the possible outcomes.
\nExperimental probability = number of times an event occurs\/ total number of times the experiment is carried out.
\nthis value changes each time an experiment is carried out.<\/p>\n

Practice & Problem Solving<\/strong><\/p>\n

Leveled Practice In 7 and 8, complete each statement.
\nQuestion 7.
\nThe table shows the results of spinning a wheel 80 times.
\nWhat is the relative frequency of the event “spin a 3”?
\n\"Envision
\nThe relative frequency of the wheel landing on 3 is
\n\\(\\frac{\\text { number of times an event occurs }}{\\text { total number of trials }}\\) = \\(\\frac{}{}\\) = _________%<\/p>\n

Answer:
\nThe relative frequency of the wheel landing on 3 is 6 times.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe table shows the results of spinning a wheel 80 times.
\nThe relative frequency of the wheel landing on 3 is
\n18\/3 = 6.
\nso the relative frequency of the wheel landing on 3 is 6 times.<\/p>\n

Question 8.
\nLiz flips a coin 50 times. The coin lands heads up 20 times and tails up 30 times. Complete each statement.
\nThe theoretical probability of the coin landing heads up is __________
\nBased on Liz’s results, the experimental probability of the coin landing heads up is __________.
\nThe theoretical probability is __________ than the experimental probability in this experiment.<\/p>\n

Answer:
\nThe theoretical probability of the coin landing heads up = 20\/50.
\nthe experimental probability of the coin landing heads up = 30\/50.
\nthe theoretical probability is less than the experimental probability in this experiment.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLiz flips a coin 50 times.
\nThe coin lands head up 20 times and tails up 30 times.
\n20 out of 50 is 20\/50.
\n30 out of 50 is 30\/50.
\nThe theoretical probability of the coin landing heads up = 20\/50.
\nthe experimental probability of the coin landing heads up = 30\/50.
\nthe theoretical probability is less than the experimental probability in this experiment.<\/p>\n

Question 9.
\nJess spins a pointer 25 times and finds an experimental probability of the pointer landing on 3 to be \\(\\frac{4}{25}\\), or 16%. The theoretical probability of the spinner landing on 3 is , or 25%. Why might there be a significant difference between the theoretical and experimental probabilities?<\/p>\n

Answer:
\nThe experimental probability is less than the theoretical probability.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJess spins a pointer 25 times and finds an experimental probability of the pointer landing on 3 to be \\(\\frac{4}{25}\\), or 16%.
\nThe theoretical probability of the spinner landing on 3 is, or 25%.
\n4\/25 = 0.16.
\n0.16\/100 = 16.
\n16 is less than 25.
\nso the experimental probability is less than the theoretical probability.<\/p>\n

Question 10.
\nThe table shows the results of a survey of 100 people randomly selected at an airport. Find the experimental probability that a person is going to City E.
\n\"Envision<\/p>\n

Answer:
\nThe experimental probability that a person is going to city E is 8\/100.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe table shows the results of a survey of 100 people randomly selected at an airport.
\ncity A is 28 responses.
\nCity B is 34 responses.
\ncity C is 16 responses.
\ncity D is 14 responses.
\ncity E is 8 responses.
\nso the experimental probability that a person is going to city E is 8\/100.<\/p>\n

Question 11.
\nThe theoretical probability of selecting a consonant at random from a list of letters in the alphabet is \\(\\frac{21}{26}\\) Wayne opens a book, randomly selects a letter on the page, and records the letter. He repeats the experiment 200 times. He finds P(consonant) = 60%. How does the theoretical probability differ from the experimental probability? What are some possible sources for this discrepancy?<\/p>\n

Answer:
\nSome possible sources for this discrepancy = 333.3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe theoretical probability of selecting a consonant at random from a list of letters in the alphabet is \\(\\frac{21}{26}\\) Wayne opens a book, randomly selects a letter on the page and records the letter.
\nHe repeats the experiment 200 times.
\nHe finds P(consonant) = 60%.
\n21\/26 = 0.8076.
\n60\/100 = 6\/10.
\n6\/10 = 0.6.
\n200\/ 0.6 = 333.3.<\/p>\n

Question 12.
\nHigher Order Thinking<\/strong> Seven different names are written onto sticks and placed into a cup. A stick is chosen 100 times, out of which the name Grace is chosen 23 times. How do the theoretical probability and experimental probability compare? Explain why there is a discrepancy between them, if there is any.
\n\"Envision<\/p>\n

Answer:
\nThe discrepancy between them is 4.347.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSeven different names are written onto sticks and placed into a cup.
\nA stick is chosen 100 times, out of which the name Grace is chosen 23 times.
\n100\/23 = 4.347.
\nso the discrepancy between them is 4.347.<\/p>\n

Question 13.
\nEach of three friends flips a coin 36 times. Angel records “tails” 20 times. Michael records “tails” 17 times. Fernanda records “tails\u201d 23 times.
\na. Find the relative frequency with which each friend records “tails”.<\/p>\n

Answer:
\nThe relative frequency with which each friend records tails is 15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEach of three friends flips a coin 36 times.
\nAngel records “tails” 20 times.
\nMichael records “tails” 17 times.
\nFernanda records “tails\u201d 23 times.
\n20 + 17 + 23 = 60.
\n60\/4 = 15.
\nso the relative frequency with which each friend records tails is 15.<\/p>\n

b. Which friend has a relative frequency that is closest to the theoretical probability of flipping “tails\u201d 36 times? Explain.<\/p>\n

Answer:
\nFernanda has a relative frequency that is closest to the theoretical probability of flipping tails.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEach of three friends flips a coin 36 times.
\nAngel records “tails” 20 times.
\nMichael records “tails” 17 times.
\nFernanda records “tails\u201d 23 times.
\n20 + 17 + 23 = 60.
\n60\/4 = 15.
\nso the relative frequency that is closest to the theoretical probability of flipping tails is Fernanda.<\/p>\n

Assessment Practice<\/strong>
\nQuestion 14.
\nIn a survey, 125 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
\n\"Envision<\/p>\n

Answer:
\nThe theoretical probability and experimental probability of choosing a card with the number 1 is 0.12 and 0.2.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIn a survey, 125 people were asked to choose one card out of five cards labeled 1 to 5.
\nthe theoretical property is 15\/125.
\n15\/125 = 0.12.
\nthe experimental property is 25\/125.
\n25\/125 = 0.2.
\nso the theoretical probability and experimental probability of choosing a card with the number 1 are 0.12 and 0.2.<\/p>\n

Question 15.
\nA basketball player makes 65% of all free throws in her first 5 seasons. In her 6th season she makes 105 out of 150 free throws. How does the observed frequency of her 6th season compare to the expected frequency? Provide a possible explanation for any similarities or differences in the frequencies.<\/p>\n

Answer:
\nThe difference is 0.57.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA basketball player makes 65% of all free throws in her first 5 seasons.
\nIn her 6th season, she makes 105 out of 150 free throws.
\n105\/150 = 0.7.
\n65\/5 = 13%.
\n0.7 – 0.13 = 0.57.
\nso the difference is 0.57.<\/p>\n

Lesson 7.4 Use Probability Models<\/h3>\n

Explain It!<\/strong><\/p>\n

The Chess Club has 8 members. A new captain will be chosen by randomly selecting the name of one of the members. Leah and Luke both want to be captain. Leah says the chance that she will be chosen as captain is \\(\\frac{1}{2}\\) because she is either chosen for captain or she is not. Luke says the chance that he is chosen is \\(\\frac{1}{8}\\).
\nI can… use probability models to find probabilities of events.
\n\"Envision<\/p>\n

A. Construct Arguments Do you agree with Leah’s statement? Use a mathematical argument to justify your answer.<\/p>\n

Answer:
\nYes, I agree with Leah’s statement.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe Chess Club has 8 members.
\nA new captain will be chosen by randomly selecting the name of one of the members.
\nLeah and Luke both want to be captains.
\nLeah says the chance that she will be chosen as captain is \\(\\frac{1}{2}\\) because she is either chosen for a captain or she is not.
\nso I agree with Leah’s statement.<\/p>\n

B. Construct Arguments Do you agree with Luke’s statement? Use . a mathematical argument to justify your answer.<\/p>\n

Answer:
\nYes, Luke was also correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe Chess Club has 8 members.
\nA new captain will be chosen by randomly selecting the name of one of the members.
\nLeah and Luke both want to be captains.
\nLuke says the chance that he is chosen is \\(\\frac{1}{8}\\).
\nso I agree with Luke’s statement.<\/p>\n

Focus on math practices
\nLook for Relationships How does the probability of Leah being chosen captain compare to the probability of Luke being chosen captain?<\/p>\n

Essential Question<\/strong>
\nHow can a model be used to find the probability of an event?<\/p>\n

Try It!<\/strong>
\nMr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
\nThe sample space _________ change. Each event within the sample space change. The probability of each event ________ change.
\nThe new probability of drawing a red marble is P(R) = \\(\\frac{1}{}\\)<\/p>\n

Answer:
\nThe sample space does not change.
\nEach event within the sample space change.
\nThe probability of each event does not change.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMr. Campbell decides that too many students are getting a pass on homework.
\nHe adds 10 yellow marbles to the jar.
\nso the sample space does not change.
\neach event within the sample space change.
\nthe probability of each event does not change.<\/p>\n

Convince Me!<\/strong> How does a probability model help you predict how likely an event is to occur?<\/p>\n

Try It!<\/strong>
\nTo reduce the number of homework passes, which color of marble should Ms. Stillman use as the pass on homework? Explain.<\/p>\n

Answer:
\nHe should use red color marbles.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nto reduce the number of homework passes,
\nhe should use red color marbles.<\/p>\n

KEY CONCEPT<\/strong>
\nA probability model can help you evaluate a chance process and its outcomes. You can develop a model using theoretical or experimental probability. A probability model consists of the sample space of an action, events within the sample space, and probabilities associated with each event.
\nFor rolling a number cube labeled from 1 through 6: Sample space, S = {1, 2, 3, 4, 5, 6}
\n\"Envision
\nP(1) = \\(\\frac{1}{6}\\)
\nP(2) = \\(\\frac{1}{6}\\)
\nP(3) = \\(\\frac{1}{6}\\)
\nP(4) = \\(\\frac{1}{6}\\)
\nP(5) = \\(\\frac{1}{6}\\)
\nP(6) = \\(\\frac{1}{6}\\)<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question How can a model be used to find the probability of an event?<\/p>\n

Answer:
\nThe probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA probability model can help you evaluate a chance process and its outcomes. You can develop a model using theoretical or experimental probability. A probability model consists of the sample space of action, events within the sample space, and probabilities associated with each event.
\nFor rolling a number cube labeled from 1 through 6: Sample space, S = {1, 2, 3, 4, 5, 6}.
\nso the probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Question 2.
\nConstruct Arguments How can you check the sample space of a probability model?<\/p>\n

Answer:
\nThe probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA probability model can help you evaluate a chance process and its outcomes. You can develop a model using theoretical or experimental probability. A probability model consists of the sample space of action, events within the sample space, and probabilities associated with each event.
\nFor rolling a number cube labeled from 1 through 6: Sample space, S = {1, 2, 3, 4, 5, 6}.
\nso the probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Question 3.
\nReasoning How does developing a probability model based on experimental probability help you evaluate a situation or make an estimate? Explain.<\/p>\n

Answer:
\nThe probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA probability model can help you evaluate a chance process and its outcomes. You can develop a model using theoretical or experimental probability. A probability model consists of the sample space of action, events within the sample space, and probabilities associated with each event.
\nFor rolling a number cube labeled from 1 through 6: Sample space, S = {1, 2, 3, 4, 5, 6}.
\nso the probability of an event is to evaluate a chance process and its outcomes.<\/p>\n

Do You Know How?<\/strong>
\nQuestion 4.
\nDevelop a probability model for the spinner shown.
\n\"Envision<\/p>\n

Answer:
\nP(1) = \\(\\frac{1}{5}\\)
\nP(2) = \\(\\frac{1}{5}\\)
\nP(3) = \\(\\frac{1}{5}\\)
\nP(4) = \\(\\frac{1}{5}\\)
\nP(5) = \\(\\frac{1}{5}\\)<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe spinner is on the 2 and 5.
\nif the spinner is on the 1 through 1\/5.
\nif the spinner is on the 2 through 2\/5.
\nif the spinner is on the 3 through 3\/5.
\nif the spinner is on the 4 through 4\/5.
\nif the spinner is on the 5 through 5\/5.<\/p>\n

Question 5.
\nMr. Henry has a basket full of fruit. He does not know how many pieces of fruit are in the basket or the types of fruit. Each of the 20 students in his class selects one piece of fruit from the basket without looking, notes its fruit type, and then puts it back in the basket. Based on the results shown in the table, what can the students conclude about the probability of selecting an apple?
\n\"Envision<\/p>\n

Answer:
\nThe probability of selecting an apple is 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMr. Henry has a basket full of fruit.
\nHe does not know how many pieces of fruit are in the basket or the types of fruit.
\nEach of the 20 students in his class selects one piece of fruit from the basket without looking, notes its fruit type, and then puts it back in the basket.
\nthe number of pieces of fruit of apple is 5.
\n20\/5 = 4.
\n4 x 5 = 20.
\nso the probability of selecting an apple is 4.<\/p>\n

Question 6.
\nThe probability model based on experimental probability for randomly selecting a marble from a bag is P(green) = \\(\\frac{18}{40}\\), P(blue) = \\(\\frac{14}{40}\\), and P(white) = \\(\\frac{8}{40}\\). About how many marbles of each color are in the bag if there are 60 total marbles?<\/p>\n

Answer:
\nThe number of marbles of each color is in the bag if there are 60 total marbles = 25, 20, and 15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\np(green) = 18\/40.
\np(blue) = 14\/40.
\np(white) = 8\/40.
\n18 + 14 + 8 = 40.
\n25 + 20 + 15 = 60.
\nso p(green) = 25.
\np(blue) = 20.
\np(white) = 15.
\nso the number of marbles of each color is in the bag if there are 60 total marbles = 25, 20, and 15.<\/p>\n

Practice & Problem Solving<\/strong><\/p>\n

Question 7.
\nMurray spins the pointer of the spinner shown at the right.
\n\"Envision
\na. What is the sample space for the probability model?<\/p>\n

Answer:
\nThe sample space for the probability model is 3\/8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMurray spins the pointer of the spinner shown at the right.
\nthe spinner is on the 3.
\np(3\/8) = 3\/8.
\nso the sample space for the probability model is 3\/8.<\/p>\n

b. What is the probability of each event in the sample space?<\/p>\n

Answer:
\nThe probability of each event in the sample space = 1\/8, 3\/8, and 5\/8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMurray spins the pointer of the spinner shown at the right.
\nif the spinner is on the 1.
\np(1\/8) = 1\/8.
\nif the spinner is on the 3.
\np(3\/8) = 3\/8.
\nso the probability of each event in the sample space = 1\/8, 3\/8, and 5\/8.<\/p>\n

Question 8.
\nRafael spins the pointers of the two spinners shown at the right. Find the probability of each possible sum.
\n\"Envision
\nP(sum 2) = __________
\nP(sum 3) = __________
\nP(sum 4) = __________
\nP(sum 5) = __________<\/p>\n

Answer:
\np(sum 2) =
\np(sum 3) =
\np(sum 4) =
\np(sum 5) =<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,<\/p>\n

Question 9.
\nBe Precise An arts and crafts store has a crate that contains glass, wood, and brass beads. Friends take turns choosing a bead without looking, recording the bead type, and returning the bead to the crate. The table shows the results of 300 selections.
\n\"Envision
\na. Write a probability model for choosing a bead.<\/p>\n

Answer:
\nThe model for choosing a bead = p(0.2), p(0.32), and p(0.48).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAn arts and crafts store has a crate that contains glass, wood, and brass beads.
\nFriends take turns choosing a bead without looking, recording the bead type, and returning the bead to the crate.
\nglass = p(60\/300) = p(0.2).
\nwood = p(96\/300) = p(0.32).
\nbrass = p(144\/300) = p(0.48).
\nso the model for choosing a bead = p(0.2), p(0.32), and p(0.48).<\/p>\n

b. Based on the frequencies in the table, estimate the number of each type of bead that will be chosen if the friends select a total of 450 beads from the crate.<\/p>\n

Answer:
\nThe friends select a total of 450 beads from the crate = p(0.2), p(0.32), and p(0.48).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAn arts and crafts store has a crate that contains glass, wood, and brass beads.
\nFriends take turns choosing a bead without looking, recording the bead type, and returning the bead to the crate.
\n60 + 40 = 100.
\n96 + 54 = 150.
\n144 + 56 = 200.
\n100 + 150 + 200 = 450.
\nglass = p(100\/450) = p(0.2).
\nwood = p(150\/450) = p(0.32).
\nbrass = p(200\/450) = p(0.48).
\nso the friends select a total of 450 beads from the crate = p(0.2), p(0.32), and p(0.48).<\/p>\n

Question 10.
\nA bag contains 14 green, 12 orange, and 19 purple tennis balls.
\na. Create a probability model for choosing a tennis ball from the bag.<\/p>\n

Answer:
\nThe probability model for choosing a tennis ball from the bag = p(0.3), p(0.2), and p(0.4).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA bag contains 14 green, 12 orange, and 19 purple tennis balls.
\n14 + 12 + 19 = 45.
\np(green) = p(14\/45).
\np(orange) = p(12\/45).
\np(purple) = p(19\/45).
\nso the probability model for choosing a tennis ball from the bag = p(0.3), p(0.2), and p(0.4).<\/p>\n

b. Suppose a tennis ball is randomly selected and then replaced 75 times. How many orange tennis balls do you expect? Explain.<\/p>\n

Answer:
\nThe number of orange tennis balls does you expert = p(20\/45).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSuppose a tennis ball is randomly selected and then replaced 75 times.
\n14 + 11 = 25.
\n12 + 8 = 20.
\n19 + 11 = 30.
\n25 + 20 + 30 = 75.
\nso the number of orange tennis balls does you expert = p(20\/45).<\/p>\n

Question 11.
\nGiven that Pred pepper) = \\(\\frac{3}{5}\\), write another probability statement to complete the probability model of a random pepper selection from the box below.
\n\"Envision<\/p>\n

Answer:
\nThe probability model of a random pepper is p(pepper) = 5\/14.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nP(red pepper) = \\(\\frac{3}{5}\\).
\ntotal there are 14 trays.
\nI chooses 5 trays.
\np(pepper) = p(5\/14).
\nso the probability model of a random pepper is p(pepper) = 5\/14.<\/p>\n

Question 12.
\nHigher Order Thinking<\/strong> A survey asked 600 people for their favorite genre of book. The table shows the number of people who preferred four possible genres.
\n\"Envision
\na. How many people surveyed responded with a genre that is not listed in the table?<\/p>\n

Answer:
\nThe number of people surveyed responded with a genre that is not listed in the table = 126.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA survey asked 600 people for their favorite genre of book.
\nthe people who selected Adventure is 90.
\nthe people who selected comedy is 102.
\nthe people who selected Mystery is 150.
\nthe people who selected Romance is 132.
\n90 + 102 + 150 + 132 = 474.
\n600 – 474 = 126.
\nso the number of people surveyed responded with a genre that is not listed in the table = 126.<\/p>\n

b. Find the probabilities and complete a probability model to describe each response, including “other genre”.<\/p>\n

Answer:
\nThe probabilities are p(0.18), p(0.21), p(0.31), and p(0.27).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA survey asked 600 people for their favorite genre of book.
\nthe people who selected Adventure is 90.
\nthe people who selected comedy is 102.
\nthe people who selected Mystery is 150.
\nthe people who selected Romance is 132.
\np(90\/474) = p(0.18).
\np(102\/474) = p(0.21).
\np(150\/474) = p(0.31).
\np(132\/474) = p(0.27).
\nso the probabilities are p(0.18), p(0.21), p(0.31), and p(0.27).<\/p>\n

Assessment Practice<\/strong>
\nQuestion 13.
\nOne hundred people buy gum balls from a gum ball machine. 45 of them get a red gum ball, 40 get a blue gum ball and 15 get a yellow gum ball.<\/p>\n

PART A<\/strong>
\nDevelop a probability model to predict the color of the next gum ball purchased. Compare the probability of getting a red gum ball to the probability of getting a yellow gum ball.<\/p>\n

Answer:
\nThe probabilities are p(0.45), p(0.4), and p(0.15).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne hundred people buy gumballs from a gumball machine.
\n45 of them get a red gumball, 40 get a blue gumball and 15 get a yellow gumball.
\np(red) = p(45\/100).
\np(blue) = p(40\/100).
\np(yellow) = p(15\/100).
\nso the probabilities are p(0.45), p(0.4), and p(0.15).<\/p>\n

PART B<\/strong>
\nOf the next 10 people to buy gum balls, 7 get yellow, 1 gets red and 2 get blue. Explain a possible reason for this outcome.<\/p>\n

Answer:
\nThe probabilities are p(0.7), p(0.1), and p(0.2).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne hundred people buy gumballs from a gumball machine.
\n45 of them get a red gumball, 40 get a blue gumball and 15 get a yellow gumball.
\np(red) = p(1\/10).
\np(blue) = p(2\/10).
\np(yellow) = p(7\/10).
\nso the probabilities are p(0.7), p(0.2), and p(0.1).<\/p>\n

Topic 7 MID-TOPIC CHECKPOINT<\/h3>\n

Question 1.
\nVocabulary How does the theoretical probability of the event “flip heads” change when a coin is flipped more times in an experiment? Lesson 7-2
\nA. increases; there are more chances for heads to be flipped
\nB. decreases; there are more chances for tails to be flipped
\nC. does not change
\nD. increases; all values increase<\/p>\n

Answer:
\nOption A is correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe theoretical probability of the event “flip heads” changes when a coin is flipped more times in an experiment.
\nso it is increased.
\nthere are more chances for heads to be flipped.
\nso option A is correct.<\/p>\n

In 2-4, use the information given. Brianna has a bag of marbles that are all the same size. Of all the marbles in the bag, there are 6 red, 7 white, 3 black, and 4 green marbles.
\nQuestion 2.
\nSelect all the likelihood statements that are true. Lesson 7-1
\n\u2610 It is impossible that Brianna will draw a blue marble.
\n\u2610 It is more likely that Brianna will draw a black marble than a green marble.
\n\u2610 It is certain that Brianna will draw either a red, white, black, or green marble.
\n\u2610 It is unlikely that Brianna will draw a black marble.
\n\u2610 It is neither likely nor unlikely that Brianna will draw a green marble.<\/p>\n

Answer:
\nOptions C, D, and E are correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBrianna has a bag of marbles that are all the same size.
\nOf all the marbles in the bag, there are 6 red, 7 white, 3 black, and 4 green marbles.
\nit is certain that Brianna will draw either a red, white, black, or green marble.
\nit is unlikely that Brianna will draw a black marble.
\nit is neither likely nor unlikely that Brianna will draw a green marble.
\nso options C, D, and E are correct.<\/p>\n

Question 3.
\nRyan asks 80 people to choose a marble, note the color, and replace the marble in Brianna’s bag. The results of the random marble selections in this experiment are: 34 red, 18 white, 9 black, and 19 green marbles. How does the theoretical probability compare with the experimental probability of drawing a white marble? Lessons 7-2 and 7-3
\n\"Envision<\/p>\n

Answer:
\nThe theoretical probability is equal to the experimental probability.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRyan asks 80 people to choose marble, note the color, and replace the marble in Brianna’s bag.
\nThe results of the random marble selections in this experiment are 34 red, 18 white, 9 black, and 19 green marbles.
\n34 + 18 + 9 + 19 = 80.
\np(white) = p(18\/80).
\np(white) = p(0.225).
\nso the theoretical probability is equal to the experimental probability.<\/p>\n

Question 4.
\nWrite a probability model for this experiment, and use the probability model to predict how many times Brianna would pick a green marble if she chose a marble 50 times. Give the probabilities as simplified fractions. Lesson 7-4
\nDrawing a red marble: __________
\nDrawing a black marble: __________
\nDrawing a white marble: __________
\nDrawing a green marble: __________
\nBrianna would draw __________ green marbles in 50 tries.<\/p>\n

Answer:
\nDrawing red marble is p(25\/50) = p(0.5).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBrianna would pick a green marble if she chose a marble 50 times.
\n34 – 9 = 25.
\n18 – 8 = 10.
\n9 – 4 = 5.
\n19 – 9 = 10.
\ndrawing red marble is p(red) = p(25\/50).
\n25\/50 = 1\/2.
\nso drawing red marble is p(0.5).<\/p>\n

Question 5.
\nJewel spins the pointer of a spinner. The spinner has 7 equal-sized sections labeled 1 to 7. What is the probability that Jewel will spin a 7? Lessons 7-2 and 7-4<\/p>\n

Answer:
\nThe probability that Jewel will spin a 7 is p(1).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJewel spins the pointer of a spinner.
\nThe spinner has 7 equal-sized sections labeled 1 to 7.
\np(7\/7) = p(1).
\nso the probability that Jewel will spin a 7 is p(1).<\/p>\n

Topic 7 MID-TOPIC PERFORMANCE TASK<\/h3>\n

Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.
\n\"Envision<\/p>\n

PART A<\/strong>
\nViet makes a probability model to describe the probability of each number being called first. Quinn makes a probability model to describe the probability of any particular letter being called first. Compare the probability models.<\/p>\n

Answer:
\nThe probability models are (1\/50), (16\/30), (31\/45), (46\/60), and (61\/75).<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nViet, Quinn, and Lucy are going to play Bingo, using a standard game set.
\nB – 1 to 15.
\nI – 16 to 30.
\nN – 31 to 45.
\nG – 46 to 60.
\nO – 61 to 75.
\nso the probability models are 1\/50), (16\/30), (31\/45), (46\/60), and (61\/75).<\/p>\n

PART B<\/strong>
\nLucy makes a probability model to determine whether the first number drawn will be even or odd. Compare the different probabilities.<\/p>\n

Answer:
\nThe first probability model is odd.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe first number drawn is odd.
\n1 – 15.
\n15\/75.
\nso the first probability model is odd.<\/p>\n

PART C<\/strong>
\nSuppose the game changed to have 90 numbers, instead of 75 numbers, matched with the letters B, I, N, G, and O. How would Viet’s, Quinn’s, and Lucy’s probability models change? Explain.<\/p>\n

Answer:
\nLucy’s probability model change is 21\/90.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nsuppose the game changed to have 90 numbers., instead of 75 numbers.
\nso the B – 1 to 21.
\nI – 22 to 36.
\nN – 37 to 51.
\nG – 52 to 66.
\nO – 67 to 90.
\nso Lucy’s probability model change is 21\/90.<\/p>\n

3-Act Mathematical Modeling: Photo Finish<\/h3>\n

ACT 1<\/strong>
\nQuestion 1.
\nAfter watching the video, what is the first question that comes to mind?
\nAnswer:<\/p>\n

Question 2.
\nWrite the Main Question you will answer.
\nAnswer:<\/p>\n

Question 3.
\nConstruct Arguments Predict an answer to this Main Question. Explain your prediction.
\n\"Envision
\nAnswer:<\/p>\n

Question 4.
\nOn the number line below, write a number that is too small to be the answer. Write a number that is too large. Plot your prediction on the same number line.
\n\"Envision<\/p>\n

Answer:
\nThe too small is 0.01 and the large is 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe number that is too small is 0.01.
\nit is the starting stage of the number line.
\nthe number that is too large is 1.
\nit is the ending stage of the number line.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-7\"<\/p>\n

ACT 2<\/strong>
\nQuestion 5.
\nWhat information in this situation would be helpful to know? How would you use that information?
\n\"Envision
\nAnswer:<\/p>\n

Question 6.
\nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
\nAnswer:<\/p>\n

Question 7.
\nModel with Math<\/strong> Represent the situation using mathematics. Use your representation to answer the Main Question.
\nAnswer:<\/p>\n

Question 8.
\nWhat is your answer to the Main Question? Is it higher or lower than your prediction? Explain why.
\n\"Envision
\nAnswer:<\/p>\n

ACT 3<\/strong>
\nQuestion 9.
\nWrite the answer you saw in the video.
\nAnswer:<\/p>\n

Question 10.
\nReasoning Does your answer match the answer in the video?
\nIf not, what are some reasons that would explain the difference?
\n\"Envision
\nAnswer:<\/p>\n

Question 11.
\nMake Sense and Persevere<\/strong> Would you change your model now that you know the answer? Explain.
\n\"Envision<\/p>\n

Answer:
\nThe answer is 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthe numbers on the figure are 1, 2, and 3.
\n1 + 2 + 3 = 6.
\nso the answer is 6.<\/p>\n

ACT 3<\/strong><\/p>\n

Reflect<\/strong>
\nQuestion 12.
\nModel with Math<\/strong> Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
\n\"Envision
\nAnswer:<\/p>\n

Question 13.
\nBe Precise<\/strong> What vocabulary have you learned in this topic that helps you communicate the answer to the Main Question?
\nAnswer:<\/p>\n

SEQUEL<\/strong>
\nQuestion 14.
\nGeneralize<\/strong> How would your answer change if a fifth person joined the race? A sixth person? If n people are running in the race?
\nAnswer:<\/p>\n

Lesson 7.5 Determine Outcomes of Compound Events<\/h3>\n

Solve & Discuss It!<\/strong><\/p>\n

Cameron packed two pairs of shorts and three T-shirts for a weekend trip. What are some combinations of shirts and shorts that Cameron can wear while on his trip? How many days will he have a different outfit to wear?
\nI can… find all possible outcomes of a compound event.
\n\"Envision<\/p>\n

Focus on math practices<\/strong>
\nReasoning How would the number of different outfits change if Cameron packed a pair of khaki shorts? Explain.<\/p>\n

Essential Question<\/strong>
\nHow can all the possible outcomes, or sample space, of a compound event be represented?<\/p>\n

Answer:
\nThe number of times the possible outcomes are 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nCameron can wear 3 t-shirts in 3 days.
\nCameron packed two pairs of shorts and three T-shirts for a weekend trip.
\nCameron can wear 3 t-shirts in 3 days.
\nso the number of times the possible outcomes are 3.<\/p>\n

Try It!<\/strong>
\nJorge will flip two quarters at the same time. Complete the tree diagram, and then list the sample space of this compound event. Use H for heads and T for tails.
\n\"Envision
\nThe sample space is:______________<\/p>\n

Answer:
\nThe missing numbers are H, H, and T.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJorge will flip two quarters at the same time.
\ntwo heads give the answer head.
\ntwo tails give the answer head.
\nso the missing numbers are H, H, and T.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-8\"<\/p>\n

Convince Me!<\/strong> How does the sample space change when the number of quarters that Jorge flips is increased by 1?<\/p>\n

Try It!<\/strong>
\nThe bag contains tiles labeled with the letters A, B, and C. The box contains tiles labeled with the numbers 1, 2, and 3. June draws one letter tile and one number tile. Represent the sample space using either a table or an organized list.
\n\"Envision<\/p>\n

Answer:
\nThe letter tiles are C\/3 and 2\/3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe bag contains tiles labeled with the letters A, B, and C.
\nThe box contains tiles labeled with the numbers 1, 2, and 3.
\nC\/3 and 2\/3.
\nso the letter tiles are C\/3 and 2\/3.<\/p>\n

KEY CONCEPT<\/strong>
\nA compound event is a combination of two or more events.
\n\"Envision
\nAn organized list, table, or tree diagram can be used to represent the sample space of a compound event. The sample space for flipping two coins consists of 4 outcomes.<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question<\/strong> How can all the possible outcomes, or sample space, of a compound event be represented?<\/p>\n

Answer:
\nA compound event is a combination of two or more events.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntwo heads are equal to one tail.
\none head and one tail are equal to head and tail.
\ntwo tails are equal to one head.
\nso compound event is a combination of two or more events.<\/p>\n

Question 2.
\nGeneralize<\/strong> Will a list, a table, and a tree diagram always give you the same number of outcomes for the same compound event? Explain.<\/p>\n

Answer:
\nYes, a table and a tree diagram always give the same number of outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntwo heads are equal to one tail.
\none head and one tail are equal to head and tail.
\ntwo tails are equal to one head.
\nso the table and a tree diagram always give the same number of outcomes.<\/p>\n

Question 3.
\nUse Structure Shari is drawing a tree diagram to represent the sample space of rolling a 12-sided game piece and spinning the pointer of a 4-section spinner. Does it matter if Shari starts the tree diagram with the game piece outcomes or the spinner outcomes? Explain.<\/p>\n

Answer:
\nThe game piece outcomes = 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nShari is drawing a tree diagram to represent the sample space of rolling a 12-sided game piece and spinning the pointer of a 4-section spinner.
\n12\/4 = 3.
\n4 x 3 = 12.
\nso the game piece outcomes = 3.<\/p>\n

Do You Know How?<\/strong>
\nQuestion 4.
\nBoth Spinner A and Spinner B have equal-sized sections, as shown at the right. Make a table to represent the sample space when both spinners are spun.
\n\"Envision<\/p>\n

Answer:
\nThe spinner A = 1, 2, and 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nBoth Spinner A and Spinner B have equal-sized sections, as shown on the right.
\nspinner B has the numbers 1, 2, and 3.
\nso the spinner A has 1, 2, and 3.<\/p>\n

Question 5.
\nTiles labeled with the letters X, Y, and Z are in a bag. Tiles labeled with the numbers 1 and 2 are in a box.
\nMake a tree diagram to represent the sample space of the compound event of selecting one tile from each container.<\/p>\n

Answer:
\nTwo x’s gives Y.
\nTwo Y’s gives Z.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTiles labeled with the letters X, Y, and Z are in a bag.
\nTiles labeled with the numbers 1 and 2 are in a box.
\n1 – x, y, and z.
\n2 – x, y, and z.
\nso two x’s give y.
\ntwo y’s gives z.<\/p>\n

Practice & Problem Solving<\/strong><\/p>\n

Leveled Practice In 6 and 7, find the number of outcomes for each event.
\nQuestion 6.
\nOliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there?
\n\"Envision
\nThere are ________ possible outcomes.<\/p>\n

Answer:
\nThere are 7 possible outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOliver is playing a game in which he has to choose one of two numbers (2 or 7).
\nand then one of five vowels (a, e, i, o, or u).
\nthe events are 1\/7, 2\/7, 3\/7, 4\/7, 5\/7, 6\/7, and 1.
\nthe vowels are a\/7, e\/7, i\/7, o\/7, and u\/7.
\nso there are 7 possible outcomes.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-9\"<\/p>\n

Question 7.
\nThere are four stores that sell school supplies (S1, S2, S3, and S4) and three stores that sell sporting goods (G1, G2, and G3) nearby. How many possible combinations of stores could you visit to buy a tennis racquet and then a backpack?
\n\"Envision
\nThere are ________ possible combinations.<\/p>\n

Answer:
\nThere are 3 possible combinations.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThere are four stores that sell school supplies (S1, S2, S3, and S4) and three stores.
\nthat sell sporting goods (G1, G2, and G3) nearby.
\nG1 – s1, s2, s3, and s4.
\nG2 – s2, s3, s4, and s1.
\nG3 – s3, s4, s3, and s2.
\nso there are 3 possible combinations.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-10\"<\/p>\n

Question 8.
\nA bakery sells wheat, multigrain, rye, and oat bread. Each type of bread is available as a loaf or as dinner rolls.
\n\"Envision
\na. Complete the table to show all the possible outcomes for the types and styles of bread sold by the bakery.<\/p>\n

Answer:<\/p>\n

b. Find the number of possible outcomes.<\/p>\n

Answer:
\nThe number of possible outcomes is 8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA bakery sells wheat, multigrain, rye, and oat bread.
\nwheat – 2 items.
\nmultigrain – 2 items.
\nrye – 2 items.
\noat bread – 2 items.
\n2 + 2 + 2 + 2 = 8.
\nso the number of possible outcomes is 8.<\/p>\n

Question 9.
\nGeneralize<\/strong> How does the number of possible outcomes of a single event help you determine the total number of possible outcomes of a compound event?<\/p>\n

Answer:
\nA compound event is a combination of two or more events.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntwo heads are equal to one tail.
\none head and one tail are equal to head and tail.
\ntwo tails are equal to one head.
\nso compound event is a combination of two or more events.<\/p>\n

Question 10.
\nA new car can be purchased with a choice of four exterior colors (A, B, C, and D) and three interior colors (1, 2, and 3). Make an organized list of all the possible color combinations for the car.<\/p>\n

Answer:
\nThe organized list of all the possible color combinations for the car is 12.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA new car can be purchased with a choice of four exterior colors (A, B, C, and D).
\nand three interior colors (1, 2, and 3).
\n4 x 3 = 12.
\n1 – A, B, C, and D.
\n2 – B, C, D, and A.
\n3 – C, D, A, and B.
\nso the organized list of all the possible color combinations for the car is 12.<\/p>\n

Question 11.
\nTwo friends each plan to order a fruit drink at the diner. The available flavors are kiwi (K), lemon (L), and watermelon (W). Make a list to represent all the possible outcomes of the friends’ fruit drink order. Write each outcome in the format (Friend 1, Friend 2).
\n\"Envision<\/p>\n

Answer:
\nEach outcome is in format 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nTwo friends each plan to order a fruit drink at the diner.
\nThe available flavors are kiwi (K), lemon (L), and watermelon (W).
\n2 friends – 3 flavors.
\n3 x 2 = 6.
\n1 – K, L, and W.
\n2 – K, L, and W.
\nso the number of outcomes is 6.<\/p>\n

Question 12.
\nPlastic souvenir cups come in three different sizes: small (S), medium (M), and large (L). The available colors are red (R), white (w), and blue (B). Make a list to represent all the possible combinations of the different cups based on size and color. Write each outcome in the format (Size, Color).<\/p>\n

Answer:
\nThe number of outcomes = 9.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nPlastic souvenir cups come in three different sizes: small (S), medium (M), and large (L).
\nThe available colors are red (R), white (w), and blue (B).
\nred – 3.
\nwhite – 3.
\nblue – 3.
\n3 + 3 + 3 = 9.
\nso the number of outcomes = 9.<\/p>\n

Question 13.
\nHigher Order Thinking<\/strong> Heidi’s older sister needs to take either Chemistry (C), Geometry (G), or Physics (P) this year. She can take the class during any one of six periods (1 through 6). Is there more than one way to draw a tree diagram to model this situation? Explain.<\/p>\n

Answer:
\nYes, there is more than one way.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nHeidi’s older sister needs to take either Chemistry (C), Geometry (G), or Physics (P) this year.
\nShe can take the class during any one of six periods (1 through 6).
\n1 – 3.
\n2 – 3.
\n3 – 3.
\n4 – 3.
\n5 – 3.
\n6 – 3.
\n3 + 3 + 3 + 3 + 3 + 3 = 18.
\nso there is more than one way.<\/p>\n

Assessment Practice<\/strong>
\nQuestion 14.
\nA fruit basket has 6 oranges, 4 apples and 2 pears in it. 5 people each select a piece of fruit and eat it. Which of the following outcomes could represent this selection?
\n\u2610 All 5 people eat an orange.
\n\u2610 1 person eats an orange, 4 people eat an apple.
\n\u2610 2 people eat an orange, 3 people eat a pear.
\n\u2610 3 people eat an orange, 1 person eats an apple, 1 person eats a pear.
\n\u2610 All 5 people eat an apple.<\/p>\n

Answer:
\nOptions B, C, and D are correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA fruit basket has 6 oranges, 4 apples, and 2 pears in it.
\n5 people each select a piece of fruit and eat it.
\n6 + 4 + 2 = 12.
\n12\/3 = 4.
\nso options B, C, and D are correct.<\/p>\n

Question 15.
\nRoyce has a collection of trading cards. 16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards. He selects half of this collection and gives them to his friend. Which of the following represent possible outcomes of this selection?
\n\u2610 He gives his friend 6 baseball cards, 10 football cards and all of his basketball cards.
\n\u2610 He gives his friend 4 baseball cards and all of his football cards.
\n\u2610 He gives his friend only football cards.
\n\u2610 He gives his friend 8 baseball cards, 10 football cards and 7 basketball cards.
\n\u2610 He gives his friend all of his baseball and basketball cards.<\/p>\n

Answer:
\nOptions B, C, and D are correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nRoyce has a collection of trading cards.
\n16 of his cards are baseball cards, 21 are football cards and 13 are basketball cards.
\n16 + 21 + 13 = 50.
\n50\/3 = 16.6.
\nso options B, C, and D are correct.<\/p>\n

Lesson 7.6 Find Probabilities of Compound Events<\/h3>\n

Solve & Discuss It!<\/strong>
\nTalia is playing a game in which she must choose Option 1 or Option 2 and then spin the game wheel, flip the coin, and roll the number cube labeled 1 through 6. For her to win a prize, all the conditions listed under the chosen option must occur. Which option should Talia choose? Explain.
\nI can… find the probability of a compound event.
\n\"Envision
\nOption 1
\n\u2022 The game wheel lands on S.
\n\u2022 The coin lands on tails.
\n\u2022 An even number is rolled.<\/p>\n

Option 2
\n\u2022 The game wheel lands on Z.
\n\u2022 The coin lands on either side.
\n\u2022 The number 3 is rolled.<\/p>\n

Answer:
\nBoth the options are correct.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nin option 1 the game wheel lands on s.
\nthe coil lands on tails.
\nan even number is rolled.
\nin option 2 the game wheel lands on z.
\nthe coin lands on either side.
\nthe number 3 is rolled.
\nso both the options are correct.<\/p>\n

Look for Relationships
\nHow can you use what you know about sample spaces to choose the best option?<\/p>\n

Focus on math practices
\nMake Sense and Persevere Suppose an Option 3 was added to the game, with the conditions that the game wheel lands on Q, the coin lands on either side, and an odd number is rolled. Should Talia change her choice to Option 3? Explain.<\/p>\n

Essential Question<\/strong>
\nHow can a model help find the probability of a compound event?<\/p>\n

Try It!<\/strong>
\nThe designer of Flip ‘n’ Spin creates a new game using a 5-section spinner, as shown. How does the new spinner change the probability of winning a prize?
\nUsing the 5-section spinner, the probability of winning a prize is ________ .
\nIt is _________ likely that a player will win a prize when using the 5-section spinner than when using the 4-section spinner.<\/p>\n

Answer:
\nIt is more likely that a player will win a prize when using the 5-section spinner than when using the 4-section spinner.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe designer of Flip ‘n’ Spin creates a new game using a 5-section spinner, as shown.
\nif it is a 4-section spinner then it gives n\/4.
\nif it is a 5 section spinner then it gives n\/5.
\nso it is more likely that a player will win a prize when using the 5-section spinner than when using the 4-section spinner.<\/p>\n

Convince Me!<\/strong> What generalization can you make about the number of sections on the spinner and the probability of winning a prize while playing the Flip ‘n’ Spin game?<\/p>\n

Try It!<\/strong>
\nIs it more likely that a coin flipped 3 times will land heads up exactly once, or will land heads up exactly 2 twice? Explain using probability.<\/p>\n

Answer:
\nYes, two heads give tails and two tails give one head.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\ntwo heads give one tail.
\ntwo tails give one head.
\nso two heads give tails and two tails give one head.<\/p>\n

Try It!<\/strong>
\nDoes Marc have a greater chance than Carly of winning the tickets to Carly? Explain using probability.
\nAnswer:<\/p>\n

KEY CONCEPT<\/strong>
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes. You can use an organized list, a table, or a tree diagram to determine the number of favorable outcomes and the total number of possible outcomes.<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question<\/strong> How can a model help find the probability of a compound event?<\/p>\n

Answer:
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.
\nwe can organize an organized list, a table, or a tree diagram to determine the number of favorable outcomes and the total number of possible outcomes.<\/p>\n

Question 2.
\nGeneralize<\/strong> What do you know about the outcomes of a compound event displayed in an organized list, a table, or a tree diagram?<\/p>\n

Answer:
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.
\nwe can organize an organized list, a table, or a tree diagram to determine the number of favorable outcomes and the total number of possible outcomes.<\/p>\n

Question 3.
\nHow does finding the probability of a compound event compare with finding the probability of a simple event?<\/p>\n

Answer:
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe probability of a compound event can be represented by a ratio of the number of favorable outcomes to the total number of possible equally likely outcomes.
\nwe can organize an organized list, a table, or a tree diagram to determine the number of favorable outcomes and the total number of possible outcomes.<\/p>\n

Do You Know How?<\/strong>
\nQuestion 4.
\nOne of three contestants will be randomly selected to win a prize. One of three different prizes will be randomly awarded to the contestant whose name is selected to win. The tree diagram shows all possible outcomes of this contest.
\n\"Envision
\nWhat is the probability that Whitney will win Prize 2?<\/p>\n

Answer:
\nThe probability that Whitney will win prize 2 is 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne of three contestants will be randomly selected to win a prize.
\nOne of three different prizes will be randomly awarded to the contestant whose name is selected to win.
\nthe contestants are Pedro, Whitney, and Bryan.
\nPedro wins 3 prizes.
\nWhitney wins 3 prizes.
\nBryan wins 3 prizes.
\nso the probability that Whitney will win prize 2 is 3.<\/p>\n

Question 5.
\nThe table shows all the possible outcomes for flipping a coin and spinning the pointer of a spinner with four equal-sized sections labeled 1 through 4.
\n\"Envision
\na. What is the probability that the pointer will stop on 3 and the coin will land on heads?<\/p>\n

Answer:
\nThe probability that the pointer will stop on 3 and the coin will land on heads = 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthere are two combinations.
\nthey are heads and tails.
\nheads 1 = 1 + 1 = 2.
\nheads 2 = 2 + 2 = 4.
\nheads 3 = 3 + 3 = 6.
\nheads 4 = 4 + 4 = 8.
\nso the probability that the pointer will stop on 3 and the coin will land on heads = 6.<\/p>\n

b. What is the probability that the pointer will stop on an odd number and the coin will land on heads?<\/p>\n

Answer:
\nThe probability that the pointer will stop on an odd number and the coin will land on heads = 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nthere are two combinations.
\nthey are heads and tails.
\nheads 1 = 1 + 1 = 2.
\nheads 2 = 2 + 2 = 4.
\nheads 3 = 3 + 3 = 6.
\nheads 4 = 4 + 4 = 8.
\nPractice & Problem Solving<\/strong><\/p>\n

Multimedia Leveled Practice in 6 and 7, find the probability of each event.
\nQuestion 6.
\nA fair coin is tossed twice in succession. The sample space is shown, where H represents heads up and T represents tails up. Find the probability of getting exactly one tail.
\n\"Envision
\nThere are _________ outcomes that have exactly one tail. There are _________ possible outcomes, which are equally likely.
\nP(exactly one tail) = __________, or _________ %<\/p>\n

Answer:
\nP(exactly one tail) = 2 or 2%.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA fair coin is tossed twice in succession.
\nThe sample space is shown, where H represents heads up and T represents tails up.
\ntoss1 and toss2.
\nin toss1 there are 2 heads, 2 tails.
\np(exactly one tail) = 2 or 2%.<\/p>\n

Question 7.
\nThe tree diagram shows the sample space of two-digit numbers that can be created using the digits 2, 6, 7, and 9. What is the probability of choosing a number from the sample space that contains both 9 and 6?
\n\"Envision
\nThere are _________ outcomes that include both 9 and 6. There are _________ possible outcomes, which are equally likely
\nP(9 and 6) = __________, or __________ %<\/p>\n

Answer:
\nThe probability of choosing a number from the sample space that contains both 9 and 6 = 4.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe tree diagram shows the sample space of two-digit numbers that can be created using the digits 2, 6, 7, and 9.
\nthe probability of choosing a number from the sample space that contains both 9 and 6:
\nin 1st diagram, there is 1 combination.
\nin the 2nd diagram, there is 1 combination.
\nin the 3rd diagram, there is 1 combination.
\nin the 4th diagram, there is 1 combination.
\nso the probability of choosing a number from the sample space that contains both 9 and 6 = 4.<\/p>\n

Question 8.
\nThe table shows the possible outcomes of spinning the given spinner and flipping a fair coin. Find the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4.
\n\"Envision<\/p>\n

Answer:
\nThe probability of the coin landing heads up and the pointer landing on 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe table shows the possible outcomes of spinning the given spinner and flipping a fair coin.
\non coin 1 the pointer landing up.
\nso the probability of the coin landing heads up and the pointer landing on 1.<\/p>\n

Question 9.
\nThe organized list shows all the possible outcomes when three fair coins are flipped. The possible outcomes of each flip are heads (H) and tails (T). What is the probability that at least 2 fair coins land heads up when 3 are flipped?
\nSample Space
\nHHT
\nHTH
\nHTT
\nTHH
\nTHT
\n\u03a4\u03a4\u0397
\nTTT<\/p>\n

Answer:
\nHHT, HTH, THH.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe organized list shows all the possible outcomes when three fair coins are flipped.
\nThe possible outcomes of each flip are heads (H) and tails (T).
\nHTH, HTH, and THH.<\/p>\n

Question 10.
\nLook for Relationships Gary spins two game wheels at the carnival. He will win a prize if both of the wheels land on any red section. How does the chance of winning change if different game wheels are used with more sections that aren’t red?
\n\"Envision<\/p>\n

Answer:<\/p>\n

Question 11.
\nModel with Math<\/strong> Each week, a clothing store gives away a shirt to a lucky customer. The shirts vary by sleeve type (Long, Short, No Sleeve) and color (Gray, Blue, Pink). Draw a tree diagram to represent the sample space. What is the probability that the free shirt will have either long or short sleeves and be either pink or blue?<\/p>\n

Answer:
\nThe probability that the free shirt will have either long or short sleeves and be either pink, blue, and gray.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nEach week, a clothing store gives away a shirt to a lucky customer.
\nThe shirts vary by sleeve type (Long, Short, No Sleeve) and color (Gray, Blue, Pink).
\nthe gray color shirt has a sleeve type and no sleeve.
\nthe blue color shirt has a sleeve type and no sleeve.
\nthe pink color shirt has a sleeve type and no sleeve.
\nso the probability that the free shirt will have either long or short sleeves and be either pink, blue, and gray.<\/p>\n

Question 12.
\nHigher Order Thinking<\/strong> The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y’s? With no O’s? Is one probability greater than the other? Explain.
\n\"Envision<\/p>\n

Answer:
\nThe probability of choosing a password with no y’s = 20.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P.
\nthere is a number of possibilities of choosing a password with no y’s.
\nthere is a number of possibilities of choosing a password with no o’s.
\nso the probability of choosing a password with no y’s = 20.<\/p>\n

Assessment Practice<\/strong>
\nQuestion 13.
\nA single number cube is rolled twice.
\nPART A
\nDetermine the number of possible outcomes. Explain how you know you have found all the possible outcomes.<\/p>\n

PART B
\nFind the probability of rolling two numbers that have a sum equal to 10.
\nAnswer:<\/p>\n

Lesson 7.7 Simulate Compound Events<\/h3>\n

Solve & Discuss It!<\/strong>
\nJillian lands the beanbag on the board in about half of her attempts in a beanbag toss game. How can she predict the number of times she will get the beanbag in the hole in her next 5 attempts using a coin toss?
\nI can… simulate a compound event to approximate its probability.
\n\"Envision<\/p>\n

Make Sense and Persevere<\/strong>
\nHow can you use what you know about the theoretical probability of landing heads-up or tails-up?<\/p>\n

Focus on math practices<\/strong>
\nUse Appropriate Tools When might it be useful to model a scenario with a coin or other tool?<\/p>\n

Essential Question<\/strong>
\nHow can you use simulations to determine the probability of events?<\/p>\n

Try It!<\/strong>
\nThere is a 50% chance that a volleyball team will win any one of its four remaining games this year. A spinner with 2 equal sections numbered 1 (win) and 2 (loss) is used to simulate the probability that the team will win exactly two of its last four games. The results of the simulation are shown below.
\n\"Envision
\n1221 1121 2211 2121 2221 2212 1122 1111 1222 1112
\nOut of 10 trials, there are _________ favorable outcomes. Based on the simulation, the probability that the team will win exactly 2 of its last 4 games is ____________.<\/p>\n

Answer:
\nOut of 10 trials, there are 10 favorable outcomes.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThere is a 50% chance that a volleyball team will win any one of its four remaining games this year.
\nA spinner with 2 equal sections numbered 1 (win) and 2 (loss).
\n1111 is the favorable outcome.
\nso out of 10 trials, there are 10 favorable outcomes.<\/p>\n

Convince Me!<\/strong> Does the probability that the team will win two games change when “exactly” is replaced with “at least”? Explain.<\/p>\n

Try It!<\/strong>
\nIn a tennis tournament, 25% of Sarah’s serves were aces. Design a simulation to predict how many aces you expect Sarah to serve out of 50 serves.<\/p>\n

Answer:
\nThe number of aces we expect Sarah to serve out of 50 serves = 2%.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIn a tennis tournament, 25% of Sarah’s serves were aces.
\n50\/25 = 2.
\nso the number of aces we expect Sarah to serve out of 50 serves = 2%.<\/p>\n

KEY CONCEPT<\/strong>
\nA simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.
\nA simulation uses a tool, such as a spinner, number cube, coin, or random number generator, for which outcomes have the same probabilities as the actual event.
\nA greater number of trials will usually give results that are closer to the theoretical probability of the actual event.<\/p>\n

Do You Understand?<\/strong>
\nQuestion 1.
\nEssential Question<\/strong> How can you use simulations to determine the probability of events?<\/p>\n

Answer:
\nThe simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA simulation uses a tool, such as a spinner, number cube, coin, or random number generator, for which outcomes have the same probabilities as the actual event.
\nA greater number of trials will usually give results that are closer to the theoretical probability of the actual event.
\nso simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Question 2.
\nLook for Relationships What is the connection between the tool used to simulate an event and the probability of the actual event?<\/p>\n

Answer:
\nThe simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA simulation uses a tool, such as a spinner, number cube, coin, or random number generator, for which outcomes have the same probabilities as the actual event.
\nA greater number of trials will usually give results that are closer to the theoretical probability of the actual event.
\nso simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Question 3.
\nWhy are the results of simulations usually close to the probabilities of their related events?<\/p>\n

Answer:
\nThe simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA simulation uses a tool, such as a spinner, number cube, coin, or random number generator, for which outcomes have the same probabilities as the actual event.
\nA greater number of trials will usually give results that are closer to the theoretical probability of the actual event.
\nso simulation is a model of a real-world situation that can be used to predict results or outcomes when the actual event is difficult to perform or record.<\/p>\n

Do You Know How?<\/strong>
\nQuestion 4.
\nCarl hits the target 50% of the time he throws a ball at it. Carl uses a coin to simulate his next three pitches. He assigns H for a hit and T for a miss. The results of 12 trials are shown below.
\nHHT HTH TTH HTT THT THH
\nHHT HTT HTH HTT TTH THT
\nBased on the results, what is the probability that Carl will hit the target with exactly two of his next three throws?<\/p>\n

Answer:
\nThe probability that carl will hit the target with exactly two of his next three throws = TTH and HHT.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nCarl hits the target 50% of the time he throws a ball at it.
\nCarl uses a coin to simulate his next three pitches.
\nHe assigns H for a hit and T for a miss.
\nthe missing trials are TTH and HHT.<\/p>\n

Question 5.
\nOn average, Margo scores a goal for her field hockey team every 2 out of 3 shots. Margo uses a number cube to simulate her next three shots. She assigns 1 to 4 as “goals” and 5 and 6 as “missed shots.” Why does this assignment of numbers on the number cube make it a valid simulation?
\n\"Envision<\/p>\n

Answer:
\nYes, it is a valid simulation.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOn average, Margo scores a goal for her field hockey team every 2 out of 3 shots.
\nMargo uses a number cube to simulate her next three shots.
\nShe assigns 1 to 4 as “goals” and 5 and 6 as “missed shots.
\nso it is a valid simulation.<\/p>\n

Practice & Problem Solving<\/strong><\/p>\n

Leveled Practice In 6 and 7, estimate the probability for each event.
\nQuestion 6.
\nMolly makes 70% of her free throws. The random numbers below represent 20 trials of a simulation of two free throws, using the numbers 0 through 9.
\n\"Envision
\nLet the numbers from \"Envision to \"Envision represent successful free throw.
\nLet the number
\nLet the numbers from \"Envision to \"Envision represent a missed free throw.
\nBased on the simulated results, the probability that Molly makes both free throws is<\/p>\n

Answer:
\nThe numbers from 3 to 21 represent a successful free throw.
\nThe numbers from 27 to 93 represent missed free throws.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nMolly makes 70% of her free throws.
\nThe random numbers below represent 20 trials of a simulation of two free throws, using the numbers 0 through 9.
\nthe numbers are 38, 38, 21, 50, 64, 71, 80, 87, 66, 92, 89, 42, 29, 89, 47, 98, 93, 90, 27, and 3.
\nso the numbers from 3 to 21 represent successful free throws.
\nthe numbers from 27 to 93 represent missed free throws.<\/p>\n

Question 7.
\nSurvey results state that 80% of people enjoy going to the beach. The random numbers below represent 10 trials of a simulation of asking two people if they enjoy going to the beach, using the numbers 0 through 9 for their responses.
\n\"Envision
\nLet the numbers from \"Envision to \"Envision represent people who enjoy going to the beach.
\nLet the numbers from \"Envision to \"Envision represent people who do not enjoy going to the beach.
\nBased on the simulated results, the probability that exactly one of two people enjoys going to the beach is \"Envision, or \"Envision%.<\/p>\n

Answer:
\nThe probability that exactly one of two people enjoys going to the beach is 80%.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nSurvey results state that 80% of people enjoy going to the beach.
\nthe numbers are 86, 53, 54, 07, 22, 65, 9, 56, 40, and 15.
\nthe numbers from 65 to 86 represent people who enjoy going to the beach.
\nthe numbers from 7 to 56 represent people who do not enjoy going to the beach.<\/p>\n

Question 8.
\nIn Stacia’s town, 60% of registered people vote regularly. A spinner with equal-sized sections numbered 0 to 9 can be used to represent those who do and do not vote.
\na. What numbers can be assigned to represent those who do vote and those who do not vote?
\nb. Based on the simulated results below, what is the probability that at least one person out of three does not vote?
\n\"Envision<\/p>\n

Answer:
\nThe numbers 799 and 851 do not vote.
\nthe numbers 117 to 768 do not vote.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nIn Stacia’s town, 60% of registered people vote regularly.
\nA spinner with equal-sized sections numbered 0 to 9 can be used to represent those who do and do not vote.
\nthe numbers are 380, 799, 331, 205, 851, 182, 117, 768, 715 and 410.
\nthe numbers 799 and 851 do not vote.
\nthe numbers 117 to 768 do not vote.<\/p>\n

Question 9.
\nInspection of items at a company shows that an item has a 50% chance of being defective. A spinner with equal-sized sections numbered 0 to 9 can be used to simulate the event that the next 2 items inspected are defective.
\n\"Envision
\na. How would you assign numbers to represent the defective and non-defective items?
\nb. Based on the simulated results below, what is the probability that the next 2 items are defective?
\n\"Envision<\/p>\n

Answer:<\/p>\n

Question 10.
\nJulie used a number cube to simulate a flower seed sprouting, for which the success rate is 50%. She used even numbers to represent success and odd numbers to represent failure. The results of 8 trials that simulate the sprouting of five seeds are shown below.
\n\"Envision
\n\"Envision
\nBased on the simulated results, what is the probability that none of the next five flower seeds will sprout successfully?<\/p>\n

Answer:
\nThe next five flower seeds will sprout successfully is 43631, 25143, 25643, and 64133.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJulie used a number cube to simulate a flower seed sprouting, for which the success rate is 50%.
\nShe used even numbers to represent success and odd numbers to represent failure.
\nthe given numbers are 31534, 35635, 43631, 35633, 25143, 25643, 64133, and 53113.
\nso the next five flower seeds will sprout successfully is 43631, 25143, 25643, 64133.<\/p>\n

Question 11.
\nConstruct Arguments How is the difference between the simulated probability and the theoretical probability of an actual event related to the number of simulated trials conducted?
\nAnswer:<\/p>\n

Question 12.
\nHigher Order Thinking<\/strong> Suppose Arun has an 80% chance of winning a game. For a simulation, the numbers 0 to 7 represent winning, and the numbers 8 and 9 represent losing. Write three different trial results that show 5 wins in a row out of 6 games played.<\/p>\n

Answer:
\nThe numbers are 1, 2, 3, 4, 5, and 6.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nArun has an 80% chance of winning a game.
\nFor a simulation, the numbers 0 to 7 represent winning, and the numbers 8 and 9 represent losing.
\n3, 4, 5, 6, 7.
\n1, 2, 3, 4, 5.
\n2, 3, 4, 5, 6.
\nso the numbers are 1, 2, 3, 4, 5, and 6.<\/p>\n

Assessment Practice<\/strong>
\nQuestion 13.
\nAbout 50% of the people surveyed in a certain county work for a small business. A random number generator was used to simulate the results of the next four people surveyed.
\nThe numbers 0 to 4 represent people who work for a small business, and the numbers 5 to 9 represent people who do not work for a small business.
\n\"Envision<\/p>\n

Answer:
\nThe numbers who work for a small business are 0501, 0403, 3074, 2235, 0803, 3750, 1288, 3154.
\nthe numbers who do not work for a small business are 6411, 7582, 7383, 5250, 7694, 9225, 7121, 7596, 8223, 8121, and 7652.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAbout 50% of the people surveyed in a certain county work for a small business.
\nA random number generator was used to simulate the results of the next four people surveyed.
\nThe numbers 0 to 4 represent people who work for a small business, and the numbers 5 to 9 represent people who do not work for a small business.
\nso the numbers who work for a small business are 0501, 0403, 3074, 2235, 0803, 3750, 1288, 3154.
\nthe numbers who do not work for a small business are 6411, 7582, 7383, 5250, 7694, 9225, 7121, 7596, 8223, 8121, and 7652.<\/p>\n

PART A<\/strong><\/p>\n

Based on the simulated results shown above, what is the probability that at least one of the next four people surveyed works for a small business?<\/p>\n

Answer:
\nThe people who surveyed works for a small business = 5250.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAbout 50% of the people surveyed in a certain county work for a small business.
\nA random number generator was used to simulate the results of the next four people surveyed.
\nThe numbers 0 to 4 represent people who work for a small business, and the numbers 5 to 9 represent people who do not work for a small business.
\nso the people who surveyed works for a small business = 5250.<\/p>\n

PART B<\/strong>
\nHow would the design of the simulation change if the percent of people who work for a small business was 70%?<\/p>\n

Answer:
\nThe number of people who work for a small business was 70% is 6411, 7582, 7383, 5250, 7694, 9225, 7121, 7596, 8223, 8121, and 7652.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nAbout 70% of the people surveyed in a certain county work for a small business.
\nA random number generator was used to simulate the results of the next four people surveyed.
\nThe numbers 0 to 4 represent people who work for a small business, and the numbers 5 to 9 represent people who do not work for a small business.
\nso the people who work for a small business were 6411, 7582, 7383, 5250, 7694, 9225, 7121, 7596, 8223, 8121, and 7652.<\/p>\n

Topic 7 REVIEW<\/h3>\n

Topic Essential Question<\/strong><\/p>\n

How can you investigate chance processes and develop, use, and evaluate probability models?<\/p>\n

Vocabulary Review<\/strong><\/p>\n

Complete each definition, and then provide an example of each vocabulary word.<\/p>\n

\"Envision<\/p>\n

\"Envision<\/p>\n

Answer:
\nThe ratio of the number of times an event occurs to the total number of trials is the probability.
\nthe set of all possible outcomes is the sample space.
\na model of a real-world situation that is used to find probabilities is a(n) is simulation.
\na single outcome or a group of outcomes is a(n) is an elementary event.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nThe ratio of the number of times an event occurs to the total number of trials is the probability.
\nfor example:
\np(red) = 7\/12.
\nthe set of all possible outcomes is the sample space.
\nfor example:
\nif the set is finite = {H, T}.
\na model of a real-world situation that is used to find probabilities is a(n) is simulation.
\nfor example:
\ndice.
\na single outcome or a group of outcomes is a(n) is an elementary event.
\nfor example:
\nsample space for a pair of dice.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-11\"<\/p>\n

Use Vocabulary in Writing
\nA restaurant serves either skim milk or whole milk in glasses that are either small, medium, or large. Use vocabulary words to explain how you could determine all the possible outcomes of milk choices at the restaurant. Use vocabulary words in your explanation.<\/p>\n

Concepts and Skills Review<\/strong><\/p>\n

Lesson 7.1 Understand Likelihood and Probability<\/strong><\/p>\n

Quick Review
\nThe probability of an event describes the likelihood an event will occur. The likelihood of an event ranges from impossible to certain, but more common descriptions are likely or unlikely. An event is a single outcome or group of outcomes. An outcome is a possible result of an action. Probability can be represented as a fraction, as a decimal, or as a percent. Something is fair if there is an equal chance for each outcome to occur.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nUse Luke’s 10-sided solid from the example. Describe an event that is certain and one that is impossible using this solid.<\/p>\n

Answer:
\nThe event describes the likelihood an event will occur.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nLuke’s 10-sided solid from the example.
\nthe event describes the likelihood an event will occur.<\/p>\n

Question 2.
\nA spinner with 8 equal-sized sections is used for a game. Based on the descriptions below, is the spinner fair? Explain. The probability the pointer will land on yellow is 1 out of 4.
\nThe probability the pointer will land on blue is 2 out of 8.
\nThe probabilities that the pointer will land on green or red are both 25%.<\/p>\n

Answer:
\nYes, the spinner is fair.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA spinner with 8 equal-sized sections is used for a game.
\nthe probability the pointer will land on blue is 2 out of 8.
\nthe probability the pointer will land on yellow is 1 out of 4.
\n2\/8 = 1\/4.
\nso the spinner is fair.<\/p>\n

Lesson 7.2 Understand Theoretical Probability<\/strong><\/p>\n

Quick Review<\/strong><\/p>\n

The theoretical probability of an event can be found if the possible outcomes are known and are all equally likely. Theoretical probability can be used to make predictions.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nUsing the example, fifteen people take out a slip of paper from the bucket without looking and record the results before replacing the slip back into the bucket. How many times is a slip labeled “5” expected to be drawn?<\/p>\n

Answer:
\nThe number of times is a slip labeled 5 is 3.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nfifteen people take out a slip of paper from the bucket without looking.
\n15\/3 = 5.
\nso the number of times is a slip labeled 5 is 3.<\/p>\n

Lesson 7.3 Understand Experimental Probability<\/strong><\/p>\n

Quick Review<\/strong>
\nThe experimental probability or relative frequency is based on actual results from an experiment and may differ from the theoretical probability of an event occurring. This discrepancy decreases as the number of trials of an experiment increases. You can use experimental probability and proportional reasoning to make predictions.
\n\"Envision<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nJaylon and Paula spin the pointer 30 times and get the results shown in the table.
\n\"Envision
\nWhat is the theoretical probability of the pointer landing on the number 2?
\nBased on the results in the table, how does the experimental probability of the pointer landing on 2 compare to the theoretical probability?<\/p>\n

Answer:
\nThe theoretical probability of the pointer landing on the number 2 is 13.
\nthe experimental probability of the pointer landing on the number 2 is 13.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJaylon and Paula spin the pointer 30 times and get the results shown in the table.
\nJaylon gets in 1st spin 6.
\n2nd spin 8, 3rd spin 9, and 4th spin 7.
\nPaula gets in 1st spin 8, 2nd spin is 5, 3rd spin is 7, and 4th spin is 10.<\/p>\n

Question 2.
\nBased on the results in the table, about how many times should Jaylon and Paula expect the pointer to land on 4 out of a total of 130 spins? Explain your answer.<\/p>\n

Answer:
\nThe pointer to land on 4 out of a total of 130 is 0.30.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nJaylon and Paula expect the pointer to land on 4 out of a total of 130 spins.
\n4\/130 = 0.30.
\nso the pointer to land on 4 out of a total of 130 is 0.30.<\/p>\n

Lesson 7.4 Use Probability Models<\/strong><\/p>\n

Quick Review<\/strong>
\nA probability model consists of a sample space, or all possible outcomes of an action, and a list of events within the sample space with the probability of each. The sum of the probabilities in the model is 1. A probability model can be used to make conclusions about probabilities of events or to make estimates or predictions.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nAbe has a different spinner. He also wants to develop a probability model.
\nHow will his probability model be the same as, and how will it differ from, Jenna’s model?
\n\"Envision<\/p>\n

Question 2.
\nWalter has a different spinner.
\n\"Envision
\nWhat is the probability that the pointer will land on a color that is not red?
\nAnswer:<\/p>\n

Question 3.
\nWhat is the sample space of Walter’s spinner?
\nAnswer:<\/p>\n

Question 4.
\nWalter will spin the pointer 50 times. About how many times will the pointer land on each color?
\nAnswer:<\/p>\n

Lesson 7.5 Determine Outcomes of Compound Events<\/strong><\/p>\n

Quick Review<\/strong>
\nA compound event is a combination of two or more events. An organized list, table, or tree diagram can be used to represent the sample space of a compound event.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nA basket contains a red, a yellow, and a green apple. A second basket contains an orange, a lemon, and a peach. Use an organized list to show all the outcomes in the sample space.<\/p>\n

Answer:
\nThe organized list to show all the outcomes in the sample space is 1.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nA basket contains a red, a yellow, and a green apple.
\nA second basket contains an orange, a lemon, and a peach.
\np(3\/3) = 1.
\nso the organized list to show all the outcomes in the sample space is 1.<\/p>\n

Question 2.
\nSimon is playing a game with letter tiles. He has 5 tiles remaining and will spell a new word by placing two tiles-first a consonant and then a vowel-in front of a Y already on the board. Complete the table below to describe all combinations of tiles that Simon can use to spell a new word.
\n\"Envision<\/p>\n

Lesson 7.6 Find Probabilities of Compound Events<\/strong><\/p>\n

Quick Review<\/strong><\/p>\n

The probability of a compound event can be represented by a ratio of the favorable outcomes to all possible outcomes. The probability can be calculated using an organized list, a table, or a tree diagram.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nOne set of cards has a beach, a road, a desert, a mountain, and an island. A second set of cards has a car, a truck, and a van. Complete the table below to find the probability of randomly drawing a mountain card and a truck card.
\n\"Envision<\/p>\n

Answer:
\nBeach = 1, 2, and 3.
\nRoad = 4, 5, and 6.
\nDesert = 7, 8, and 9.
\nMountain = 10, 11, and 12.
\nIsland = 13, 14, and 15.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nOne set of cards has a beach, a road, a desert, a mountain, and an island.
\nThe second set of cards has a car, a truck, and a van.
\nBeach = 1, 2, and 3.
\nRoad = 4, 5, and 6.
\nDesert = 7, 8, and 9.
\nMountain = 10, 11, and 12.
\nIsland = 13, 14, and 15.
\n\"Envision-Math-Common-Core-7th-Grade-Answers-Key-Topic-7-Probability-12\"<\/p>\n

Lesson 7.7 Simulate Compound Events<\/strong><\/p>\n

Quick Review<\/strong><\/p>\n

An actual event is sometimes difficult to perform or record. A simulation can be used to model the outcomes of a real-world event. Based on simulated results, you can approximate the probability and predict the future outcomes of an event.<\/p>\n

Practice<\/strong><\/p>\n

Question 1.
\nFelix’s favorite cereal includes 1 of 3 different prizes inside each box. The chance of getting each prize is equally likely. Felix conducts a simulation to see what his chances are of collecting all 3 prizes if he buys 5 boxes over time. Each section of the spinner represents the possible prizes in a single box.
\n\"Envision
\nBased on the simulation, what is the probability that Felix will collect all three prizes?<\/p>\n

Answer:
\nThe spinner represents the possible prizes in a single box = GBGBG, BGGYG, BGBYB, GYBYY, and YYGYG.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nFelix’s favorite cereal includes 1 of 3 different prizes inside each box.
\nThe chance of getting each prize is equally likely.
\nFelix conducts a simulation to see what his chances are of collecting all 3 prizes if he buys 5 boxes over time.
\nThe spinner represents the possible prizes in a single box = GBGBG, BGGYG, BGBYB, GYBYY, and YYGYG.<\/p>\n

Question 2.
\nReece is playing a carnival game in which he must guess under which of 2 cups a ball is hidden. To simulate the results of this game, he flips a coin with heads up (H) representing wins and tails up (T) representing losses. Based on the simulation below, what is the probability that Reece will win at least 2 of his next 4 games?
\n\"Envision<\/p>\n

Answer:
\nThe probability of representing the win of games is p(2) are HHTH and HHHT.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\nReece is playing a carnival game in which he must guess under which of 2 cups a ball is hidden.
\nto simulate the results of this game, he flips a coin with heads up(H) representing wins and tails up(T) representing losses.
\nHH HT and HHTH represent the win of games.
\nso the probability of representing the win of games is p(2).<\/p>\n

Topic 7 Fluency Practice<\/h3>\n

Hidden Clue<\/strong><\/p>\n

For each ordered pair, one coordinate is given. Find the second coordinate by determining the sale price after the percent markup or markdown. Then locate and label the corresponding point on the graph. Draw line segments to connect the points in alphabetical order. Use the completed picture to help you answer the riddle below.
\n\"Envision
\nA (13, 25% markup on $4). 13, \"Envision
\nB (30% markdown on $10, 1) \"Envision, 1
\nC (20% markdown on $1.25, 5) \"Envision, 5
\nD (6, 40% markdown on $5.10) 6, \"Envision
\nE (35% markup on $4, 9) \"Envision, 9
\nF (4, 50% markdown on $18.50) 4, \"Envision
\nG (60% markup on $2.50, 11) \"Envision, 11
\nH (6, 25% markdown on $15) 6, \"Envision
\nI (60% markup on $4, 13) \"Envision, 13
\nJ (8, 30% markdown on $18) 8, \"Envision
\nK (50% markup on $5.30, 11) \"Envision, 11
\nL (10,45% markdown on $20) 10, \"Envision
\nM (35% markup on $7.60, 9) \"Envision, 9
\nN (8, 30% markdown on $13) 8, \"Envision<\/p>\n

Answer:
\nA.13, 1.
\nB. 30, 1.
\nC. 0.25, 5.
\nD. 2.04, 6.
\nE. 1.4, 9.
\nF. 9.25, 4.
\nG. 1.5, 11.
\nH. 3.75, 6.
\nI. 2.4, 13.
\nJ. 5.4, 8.
\nK. 2.65, 11.
\nL. 9, 10.
\nM. 2.66, 9.
\nN. 3.9, 8.<\/p>\n

Explanation:
\nIn the above-given question,
\ngiven that,
\n25\/100 = 0.25 x 4 = 1.
\n30\/100 = 0.3 x 10 = 3.
\n20\/100 = 0.2 x 1.25 = 0.25.
\n40\/100 = 0.4 x 5.10 = 2.04.
\n35\/100 = 0.35 x 4 = 1.4.
\n50\/100 = 0.5 x 18.50 = 9.25.
\n60\/100 = 0.6 x 2.50 = 1.5.
\n25\/100 = 0.25 x 15 = 3.75.
\n60\/100 = 0.6 x 4 = 2.4.
\n30\/100 = 0.3 x 5.18 = 5.4.
\n50\/100 = 0.5 x 5.30 = 2.65.
\n45\/100 = 0.4 x 20 = 8.
\n35\/100 = 0.35 x 7.60 = 2.66.<\/p>\n","protected":false},"excerpt":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 7 Answer Key\u00a0Topic 7 Probability\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 7th Grade Answers Key Topic 7 Probability GET READY! Review What You Know! Vocabulary Choose the best term from the box to complete each definition. Question 1. A(n) _________ is a drawing …<\/p>\n","protected":false},"author":1,"featured_media":25567,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/09\/Envision-Math-Common-Core-Grade-7-Answer-Key-Topic-7-Probability.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/3155"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=3155"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/3155\/revisions"}],"predecessor-version":[{"id":27898,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/3155\/revisions\/27898"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25567"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=3155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=3155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=3155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}