Question 204955: I am having trouble with this:
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 fo the tickets.
a)Find the expected value.
b)Find the fair price of the ticket.
So far, for a, I think you would do something like this:
1st prize: 1/500 = 0.002
2nd prize: 1/500 = 0.002
3rd prize: 3/500 = 0.006
so, $300(0.002) + $200(0.002) + $50(0.006) = $1.30
For b, I do not know where to begin.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a) Good job so far, but you're forgetting to subtract the price to play the game. You need to subtract $2 from $1.30 to get: 1.3-2=-0.7
So you lose $0.70 (70 cents) on average each time you play.
b) In order for it to be a fair game, the price to play must be equal to the amount of money you lose. This way, their difference will be zero. Note: a 'fair game' is where you neither win money or lose money (ie you break even). So the fair price is $1.30 since (expected gain - price to play = 1.30 - 1.30 = 0)
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I am having trouble with this:
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 fo the tickets.
a)Find the expected value.
b)Find the fair price of the ticket.
So far, for a, I think you would do something like this:
1st prize: 1/500 = 0.002
2nd prize: 1/500 = 0.002
3rd prize: 3/500 = 0.006
so, $300(0.002) + $200(0.002) + $50(0.006) = $1.30
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You have forgotten that the buyer might not win any prize.
The probability of that happening is (495/500)
Then E(x) = $298(0.002) + $198(0.002) + $48(0.006) -2(495/500) =
[298 + 198 + 3*48 -2*495)/500 = -70 cents
The buyer can expect to lose 70 cents when he pays $2 for a ticket.
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b)Find the fair price of the ticket.
A "Fair" price would result in the buyer and the seller having
an expected gain/loss of zero.
For this game the buyer should pay $2-0.70 = @1.30 per ticket.
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Cheers,
Stan H.
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