Name Date Class. b. Suppose 24 contestants choose and replace a block from the bucket. How much money can the game show expect to pay out?

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1 1CE Exercise 10 Investigation In the ee Whiz Everyone Wins! game show, members of the audience choose a block at random from the bucket shown at the right. If a blue block is chosen, the contestant wins $5. If a red block is chosen, the contestant wins $10. If the yellow block is chosen, the contestant wins $50. The block is replaced after each turn. Color mount Won lue $5 ed $10 Yellow $50 a. What is the probability of choosing each color (from the bucket)? a. lue: Y a. ed: a. Yellow: a. Explain your method. HINT How many total blocks are there in the bucket above? How many are blue? How many are red? How many are yellow? b. Suppose 24 contestants choose and replace a block from the bucket. How much money can the game show expect to pay out? Using the probabilities you found in part (a), if 24 contestants choose a block, how many people do you expect to choose a blue block? How much does a contestant win if he/she chooses a blue block? How much would the game show have to pay if all the people expected to choose a blue block chose a blue block? If there are 24 contestants, how many do you expect to choose a red block? How much does a contestant win if he/she chooses a red block? How much would the game show have to pay if all the people expected to choose a red block chose a red block? How much does a contestant win if he/she chooses a yellow block? How much would the game show have to pay if all the people expected to choose a yellow block chose a yellow block? 115

2 2CE Exercise 23 Investigation Fergus designs two more dartboards for the school carnival. HINT See your teacher for a copy of both dartboards for you to divide into sections to help you answer the questions. Dartboard 1 Dartboard 2 a. What is the probability of landing in sections marked on Dartboard 1? On Dartboard 2? a. Dartboard 1: a. Dartboard 2: Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. 116

3 2CE Exercise 23 (continued) Investigation 2 b. player pays $1 to play, and wins $2 if the dart lands in sections marked. If the dart lands in sections marked, the player wins no money. i. How much money will the player expect to make (or lose) after 36 turns using Dartboard 1? How much money will the player expect to make (or lose) after 36 turns using Dartboard 2? HINT What is the probability of landing in a section marked on Dartboard 1? What is the probability of landing in a section marked on Dartboard 2? How much money does a player pay to play 36 times? emember that the cost to play must be subtracted from what each player makes. Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. ii. How much money will the carnival expect to make (or lose) after 36 turns using Dartboard 1? ii. How much money will the carnival expect to make (or lose) after 36 turns using Dartboard 2? c. Can the carnival expect to make a profit on this game with either board? 117

4 3CE Exercise 3 Investigation 3 Use the information in the table. It shows statistics for some of the players on a basketball team. Free-Throw Statistics Name Free Throws ttempted Free Throws Made Percent Made errit David Ken lex a. Which player has the best chance of making his next free throw? Explain your reasoning. HINT Doing part (b) first could help you answer this question. b. What is the free-throw probability for each player? errit: Ken: David: lex: Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. 118

5 4CE Exercise 1 Investigation 4 1. It costs 6 tickets to play the Toss-a-Penny game at the school carnival. For each turn, a player tosses a penny 3 times. If the penny lands heads up 2 or more times in a turn, the player wins 10 tickets to spend on food and games. a. Suppose enito plays the game 80 times. How many tickets can he expect to win? Either, complete the list of combinations that can occur if you flip a penny 3 times, H, H, T H, T, H or, finish this tree diagram. H T Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. b. What is the average number of tickets enito can expect to win or lose per turn? What is the probability that enito will get 2 heads in his 3 flips of the penny? How many games out of 80 is that probability? How many tickets would it cost enito to play 80 times? emember that enito gets 10 tickets every time he wins. ased on the number of games he is expected to win, how many tickets will he win in total? HINT emember it costs 6 tickets to play once. ased on the amount of tickets it costs enito to play 80 games and the tickets he would receive if he won, how many tickets would he expect to have at the end of 80 games? 119

6 Check-Up For use after Investigation 1 1. eoffrey is babysitting his little sister Sara and her two friends, Cela and Katie. Sara is wearing red, Cela is wearing blue and Katie is wearing green. eoffrey fills a bucket with 12 red marbles, 8 blue marbles and 4 green marbles. He tells the girls that they will play a new game. He will reach into the bucket and pull out a marble at random. The girl whose clothes match the color of the marble scores 1 point. Marble Color ed lue reen Number in ucket a. What is the probability of each girl scoring 1 point on the first draw? HINT emember: Sara is wearing red, Cela blue, and Katie green. Sara: Cela: Katie: b. What is the probability of not drawing a green marble on the first draw? c. If 2 marbles of each color are added to the bucket, do the probabilities in part (a) change? HINT Fill in the new chart to show how many of each color are now in the bucket. Marble Color ed lue reen Number in ucket Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. 120

7 Check-Up (continued) For use after Investigation 1 With the marbles added, what is the probability now of each girl scoring 1 point? Sara: Cela: Katie: Do the probabilities change from what they were in part (a)? Explain why or why not. d. If the number of marbles of each color in part (a) is doubled, do the probabilities change from what they were in part (a)? Pearson Education, Inc., publishing as Pearson Prentice Hall. ll rights reserved. Marble Color Number in ucket What is the probability now of each girl scoring 1 point? Sara: Cela: Katie: Do the probabilities change from what they were in part (a)? Explain why or why not. ed lue reen HINT Fill in the new chart to show how many of each color would be in the bucket if you doubled what you started with. 121