Question 420418: Hello, I have a question that I could use some assistance on.
Raffle tickets. 1,000 raffle tickets are sold for $1.00 each. One prize of $800.00 is to be awarded.
a) Reng Condos purchases one ticket. Determine her expected value.
b) Determine the fair price of a ticket.
Thank you so much for your help!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Raffle tickets. 1,000 raffle tickets are sold for $1.00 each.
One prize of $800.00 is to be awarded.
a) Reng Condos purchases one ticket. Determine her expected value.
Random gain values: 799, -1
Corresponding Probs: 1/1000, 999/1000
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E(x) = (1/1000)799 -1(999/1000) = (799-999)/1000 = -200/1000 = -20 cents
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b) Determine the fair price of a ticket.
Let the cost to play be "x".
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Random gain values: 800-x and -x
Corresponding Probs 1/1000 , 999/1000
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Note: A fair price means E(x) = 0
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Solve:
(800-x)/1000-999x/(1000) = 0
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800-x-999x = 0
800-1000x = 0
x = 8/10 = $0.8 = 80 cents
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Cheers,
Stan H.
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