Question 729303: Two dice are rolled in a game you pay $1.00 to play. If a total lower than 5 comes up, you win $5.00, if a total greater than 9 comes up you win $2.00, otherwise you lose your dollar for playing. Calculate the expected value of playing,and the price of the game making it fair.
Good luck, I'm not einstein.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Two dice are rolled in a game you pay $1.00 to play.
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If a total lower than 5 comes up, you win $5.00,
ways to do that: 1/1,1/2,1/3,2/1,2/2,3/1 -----6 ways
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if a total greater than 9 comes up you win $2.00,
Ways to do that:
4/6----------------------1
5/5,5/6------------------2
6/4,6/5,6/6--------------3
Total-----------------------------------------6 ways
otherwise you lose your dollar for playing.
Total-----------------------------------------24 ways
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Calculate the expected value of playing,
Random Value:.....$4......$1......-1
Probabilities.....1/6.....1/6.....4/6
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Expected gain: (4 + 1 - 4)/6 = 1/6 or 16 2/3 cents
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and the price of the game making it fair.
You should pay $1.67 to play
Then your expected winning would be zero and the game would be fair.
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Cheers,
Stan H
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