690 CHAPTER 11 Probability Spinners In Exercises 49–52, assume that a person spins the pointer and is awarded the amount indicated by the pointer. If it costs $2 to play the game, determine a) the expectation of a person who plays the game. b) the fair price to play the game. 49. $1 $10 50. $1 $10 $5 51. $1 $5 $10 $1 52. $1 $5 $10 $1 $10 Challenge Problems/Group Activities 53. Term Life Insurance An insurance company will pay the face value of a term life insurance policy if the insured person dies during the term of the policy. For how much should an insurance company sell a 10-year term policy with a face value of $40,000 to a 30-year-old man for the company to make a profit? The probability of a 30-yearold man living to age 40 is 0.97. Explain your answer. Remember that the customer pays for the insurance before the policy becomes effective. An amount greater than $1200 54. Lottery Ticket Is it possible to determine your expectation when you purchase a lottery ticket? Explain. No, you do not know how many others are selecting the same numbers you are picking. Roulette In Exercises 55 and 56, use the following roulette wheel. A roulette wheel typically contains slots with numbers 1–36 and slots marked 0 and 00. A ball is spun on the wheel and comes to rest in one of the 38 slots. Eighteen numbers are colored red, and 18 numbers are colored black. The 0 and 00 are colored green. If you bet on one particular number and the ball lands on that number, the casino pays off odds of 35 to 1. If you bet on a red number or black number and win, the casino pays 1 to 1 (even money). a) $3.50 b) $5.50 a) $4.50 b) $6.50 a) $2.25 b) $4.25 a) $3.38 b) $5.38 2 1435 0 23 4 163321 6 183119 8 122925102700 1 133624 3 153422 5 173220 7 113026 9 28 55. Determine the expected value of betting $1 on a particular number. − − $0.053, or 5.3¢ 56. Determine the expected value of betting $1 on red. −$0.053, or −5.3¢ Recreational Mathematics 57. Wheel of Fortune The following is a miniature version of the Wheel of Fortune. When Dave spins the wheel, he is awarded the amount on the wheel indicated by the pointer. If the wheel points to Bankrupt, he loses the total amount he has accumulated and also loses his turn. Assume that the wheel stops on a position and that each position is equally likely to occur. $600 Lose a turn $700 $300 $100 Bankrupt $800 $400 $200 $500 $1000 $900 a) Determine Dave’s expectation when he spins the wheel at the start of the game (he has no money to lose if he lands on Bankrupt). $458.33 b) If Dave presently has a balance of $1800, determine his expectation when he spins the wheel. $308.33
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