SOLUTION: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair
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Question 274643: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair?
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Let the cost to play be "x" dollars.
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Random gain values: 5-x ; 2-x ; -x
Probabilities::::: 8/52 ; 13/52 ; 31/52
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Note: If the game is fair expected gain should be zero.
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Equation:
E(x) = (8/52)(5-x) + (13/52)(2-x) + (31/52)x = 0
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Multiply thru by 52 to get:
[40 - 8x + 26 - 13x + 31x) = 0
10x - 66 = 0
x = $6.60 (amount you should pay to play the game)
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Cheers,
Stan H.
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