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8. A game consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is a "fair" price to pay to play? (What is the expected value of one play?)

8. A game consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is a "fair" price to pay to play? (What is the expected value of one play?)

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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Please answer 8-9. Please show work, and please be neat. 

6. A raffle is held by the MTHS ASB to draw for a $1000 plasma television. Two thousand tickets are sold at $1.00 each. Find the expected value of one ticket. 7. A game consists of flipping two coins. If both coins turn up heads, you win $1.00. What is a "fair" price to pay to play? (What is the expected value of one play?) 8. A game consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is a "fair" price to pay to play? (What is the expected value of one play?) 9. A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. Would you play the game? Why or why not? 10. Suppose you were given one of thirty free tickets at the beginning of this class period. Suppose at the end of this period (just dreaming) three tickets are drawn without replacement. The holder of the first ticket drawn wins $100, the second ticket $50, and the third ticket $30. (a) Determine your expected winnings. (b) If your neighbor offered to buy your ticket before drawing, what would be a "fair price"? 11. A company believes it has a 40% chance of being successful on bidding a contract that yields a profit of $30,000. Assume it costs $5,000 in consultant fees to prepare the bid. What is the expected gain or loss for the company if it decides to bid on the contract? 12. A department store wants to sell eight purses that cost the store $40 each and 32 purses that cost the store $10 each. If all purses are wrapped in forty identical boxes and if each customer picks a box randomly, find: (a) each customer's expected value if a customer pays $15 for a box. (b) the department store's total expected profit (or loss) during this sale. 13. Assume that the odds against a certain horse winning a race are 5 to 2. If a bettor wins $14 when the horse wins, how much should the person bet to make the game "fair"?
Transcribed Image Text:6. A raffle is held by the MTHS ASB to draw for a $1000 plasma television. Two thousand tickets are sold at $1.00 each. Find the expected value of one ticket. 7. A game consists of flipping two coins. If both coins turn up heads, you win $1.00. What is a "fair" price to pay to play? (What is the expected value of one play?) 8. A game consists of rolling a colored die with three green sides, two red sides, and one blue side. A roll of a red loses. A roll of blue pays $6.00. A roll of green pays $2.00. What is a "fair" price to pay to play? (What is the expected value of one play?) 9. A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. Would you play the game? Why or why not? 10. Suppose you were given one of thirty free tickets at the beginning of this class period. Suppose at the end of this period (just dreaming) three tickets are drawn without replacement. The holder of the first ticket drawn wins $100, the second ticket $50, and the third ticket $30. (a) Determine your expected winnings. (b) If your neighbor offered to buy your ticket before drawing, what would be a "fair price"? 11. A company believes it has a 40% chance of being successful on bidding a contract that yields a profit of $30,000. Assume it costs $5,000 in consultant fees to prepare the bid. What is the expected gain or loss for the company if it decides to bid on the contract? 12. A department store wants to sell eight purses that cost the store $40 each and 32 purses that cost the store $10 each. If all purses are wrapped in forty identical boxes and if each customer picks a box randomly, find: (a) each customer's expected value if a customer pays $15 for a box. (b) the department store's total expected profit (or loss) during this sale. 13. Assume that the odds against a certain horse winning a race are 5 to 2. If a bettor wins $14 when the horse wins, how much should the person bet to make the game "fair"?
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