SOLUTION: Question 24
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 sel
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Question 1129005: Question 24
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 1200012000 and the probability that any given ticket is selected for the $500 prize is 2200022000. Jeremy 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!
P(winning 1st prize) = 1/2000
payout for winning first prize: -$3 + $1000 = +$997
P(winning a 2nd prize) = 2/2000
payout for winning a second prize: -$3 + $500 = +$497
P(winning no prize) = 1997/2000
payout for winning no prize: -$3
A. Expected value
The expected value is the sum of the products of the probability of each outcome and the payout for that outcome:
ANSWER: The expected value for one ticket is -$2.
While that is the classic way of computing an expected value based on the definition, there is an easier path to the answer.
The total ticket sales was 2000*$3 = $6000; the total payout was $2000. That means 2/3 of every dollar spent on a ticket will NOT win a prize; 2/3 of the $3 cost of a ticket is $2.
B. The fair price of a ticket
The fair price is the price at which the total payout is equal to the total cost of the tickets. Since the total payout is $2000, for a fair ticket price, the total ticket sales should be $2000. 2000 tickets sold with a total ticket price of $2000 means $1 per ticket.
ANSWER: The fair price for a ticket is $1.
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