Question 1129581
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a. expected value for one ticket<br>
The expected winnings on one ticket are<br>
{{{(1/10000)*5000+(1/10000)*2500+(2/10000)*1000+(9996/10000)*0 = 9500/10000 = 0.95}}}<br>
The cost of the ticket is $5; the expected winnings are $0.95.  The expected value of the ticket is -$4.05.<br>
b. fair price of a ticket<br>
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.<br>
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.<br>
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.