Question 1129581: 5. 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 110,000110,000, the probability that any given ticket is selected for the $2500 prize is 110,000110,000, and the probability that any given ticket is selected for a $1000 prize is 210,000210,000.
Sidhardt purchases one of these tickets.
a. Determine his expected value.
b. Determine the fair price of a ticket.
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
a. expected value for one ticket
The expected winnings on one ticket are
The cost of the ticket is $5; the expected winnings are $0.95. The expected value of the ticket is -$4.05.
b. fair price of a ticket
The ticket price is fair (the raffle makes no money) if the cost of the tickets is equal to the total amount of the prizes.
The total amount of the prizes is $9500; the number of tickets is 10,000. A fair price for a ticket is $9500/10000 = $0.95.
Alternatively, the ticket price is fair if the cost of the ticket is equal to the expected winnings. Since the expected winnings for one ticket is $0.95, that is the fair price of a ticket.
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