11.3 Expected Value (Expectation) 689 a) Romeo’s expectation if he purchases 1 ticket. $2.00 − b) Romeo’s expectation if he purchases 10 tickets. $20.00 − 38. Foodbank Fundraiser At a fundraiser for a local foodbank, 1000 raffle tickets are sold for $10 each. One grand prize of $2000 and three consolation prizes of $100 will be awarded. Assume the probability that any given ticket selected for the grand prize is 1 1000 and the probability that any given ticket selected for a consolation prize is . 3 1000 Determine a) Jaire’s expectation if he purchases 1 ticket. $7.70 − b) Jaire’s expectation if he purchases 20 tickets. $154.00 − 39. Real Estate Listing See Example 4. Darya is a real estate broker with a house listing. Darya estimates that this listing will cost her $2400 for various expenses. If Darya sells the house within 6 months, she will receive a commission of $20,000. If she does not sell the house within 6 months, the listing will expire, and she will not receive a commission, but she still must pay the $2400 for various expenses. Darya estimates the probability that she sells the house within 6 months is 80%. Determine Darya’s expectation for this listing. $13,600 40. Real Estate Listing See Example 4. Shelby is a real estate broker with a house listing. Shelby estimates that this listing will cost him $3000 for various expenses. If Shelby sells the house within 6 months, he will receive a commission of $25,000. If he does not sell the house within 6 months, the listing will expire, and he will not receive a commission, but he still must pay the $3000 for various expenses. Shelby estimates the probability that he sells the house within 6 months is 85%. Determine Shelby’s expectation for this listing. $18,250 Dart Board In Exercises 41 and 42, assume that you are blindfolded and throw a dart at the following dart board. Assume that your dart sticks in the dart board, and not on a line. a) Determine the probabilities that the dart lands on $1, $10, $20, and $100, respectively. b) If you win the amount of money indicated by the section of the board where the dart lands, determine your expectation when you throw the dart. 41. $1 $10 $20 $1 $100 a) 9 16 , 1 4 , 1 8 , 1 16 b) $11.81 42. $1 $10 $20 $20 $100 $1 a) 5 12 , 1 6 , 7 24 , 1 8 b) $20.42 43. Fair Price The expected value of a carnival game is −$4.50, and the cost to play the game is $10.00. Determine the fair price to play the game. $5.50 44. Fair Price The expected value when you purchase a lottery ticket is −$2.00, and the cost of the ticket is $5.00. Determine the fair price of the lottery ticket. $3.00 45. Raffle Tickets Five hundred raffle tickets are sold for $3 each. One prize of $500 is to be awarded. Raul purchases one ticket. a) Determine his expected value. −$2.00 b) Determine the fair price of a ticket. $1.00 46. Raffle Tickets One thousand raffle tickets are sold for $2 each. One prize of $600 is to be awarded. Rena purchases one ticket. a) Determine her expected value. −$1.40 b) Determine the fair price of a ticket. $0.60 47. Raffle Tickets Two thousand raffle tickets are sold for $3 each. Three prizes will be awarded: one for $1000 and two for $500. Assume that the probability that any given ticket is selected for the $1000 prize is 1 2000 and the probability that any given ticket is selected for the $500 prize is . 2 2000 Jeremy purchases one of these tickets. a) Determine his expected value. −$2.00 b) Determine the fair price of a ticket. $1.00 48. Raffle Tickets Ten thousand raffle tickets are sold for $5 each. Four prizes will be awarded: one for $5000, one for $2500, and two for $1000. Assume that the probability that any given ticket is selected for the $5000 prize is , 1 10,000 the probability that any given ticket is selected for the $2500 prize is , 1 10,000 and the probability that any given ticket is selected for a $1000 prize is . 2 10,000 Sidhardt purchases one of these tickets. a) Determine his expected value. −$4.05 b) Determine the fair price of a ticket. $0.95
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