Problem 2 (20 points). Suppose that in a separate Holiday gift raffle, you purch
ID: 3323710 • Letter: P
Question
Problem 2 (20 points). Suppose that in a separate Holiday gift raffle, you purchase three tickets for a chance to win a $65 coffee maker, a great gift for Mom! You have three maker chances to win at most one coffee a) Suppose that your probability of winning on each ticket is 0.1. The purchase price of all three tickets IS 510. ls it worthwhile to take the risk and purchase the raffle tickets or just buy the coffee maker separately for $65? b) What is the maximum price you would be willing to pay for the three raffle tickets?Explanation / Answer
a) Probability that we dont win the coffee maker is computed as:
= (1 - 0.1)3 = 0.729
Therefore the probability that we win the coffee maker = 1 - Probability that we dont win the coffee maker = 0.271
Therefore expected value of the raffle
= -30 + 65*0.271
= -12.385
Therefore instead of playing the raffle, one should buy the coffee maker instead.
b) Let the maximum price that we should be willing to pay be K for each ticket. Then, we have here:
-3K + 65*0.271 = 0
K = 17.615 / 3 = 5.8717
Therefore 5.8717 is the maximum price that we would be willing to pay here.