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A casino owner decides to charge $3 to play the following game. 3 cards are drawn...

A casino owner decides to charge $3 to play the following game. 3 cards are drawn from a deck of 52. If no hearts are drawn the player gets nothing; if 1 heart is drawn the player wins $1.50; if 2 hearts are drawn the player wins $7.

How high should the owner make the jackpot on a pull of 3 hearts if he wants the house(casino) to average 60 cents a play

math   Statistics-And-Probability   
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Answer #1

p(0 ♥) = 39C3 / 52C3 = 9139/22,100 = 0.41353
p(1 ♥) = 13 • 39C2 / 52C3 = 9633/22,100 = 0.43588
p(2 ♥) = 13C2 • 39 / 52C3 = 3042/22,100 = 0.13765
p(3 ♥) = 13C3 / 52C3 = 286/22,100 = 0.01294

expected value(to player) = sum of (payoffs x probabilities) - charge
expected value(to house) = charge - sum of pxp
0.60 = 3 - 0 ( 0.41353) - 1.50 ( 0.43588) - 7 ( 0.137665) - Jackpot ( 0.01294)
0.60 = 3 - 0 - 0.65382 - 0.96355 - 0.01294J
0.60 = 1.38263 - 0.01294J
0.01294 J = 0.78263
J = $60.48

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