Question 204460: 500 tickets for prizes are sold for $2 each. Five prizes will be awarded – one for $300, one for $200, and three for $50. Steven purchases one of the tickets.
a) Find the expected value
b) Find the fair price of the ticket.
Not very good at these Word Problem things, but I am really trying to learn... If you don't mind showing me exactly how to do it I would really appreciate it. I really hate not getting things right the first time, but I am having alot of trouble with these word problems...
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 500 tickets for prizes are sold for $2 each. Five prizes will be awarded – one for $300, one for $200, and three for $50. Steven purchases one of the tickets.
a) Find the expected value
Let the random variable be "gain for Steven".
Then the vales of x are : 298,198,48,-2
The corresponding probabilities are: 1/500,1/500,3/500,495/500
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The expected gain for Steven = 298(1/500) + 198(1/500) + 48(3/500) -2(495/500)
= (298 + 198 + 3*48 - 2*495)/500 = -70 cents
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Steven can expect to lose 70 cents
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b) Find the fair price of the ticket.
He should pay (2-0.70) = $1.30 to play the game.
Then his expected winnings would be zero and his expected loss would be zero.
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Cheers,
Stan H.
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