SOLUTION: For a fair game what should be the charge to play if there is a .003 probability to win $1,000, .007 probability to win $100, and .99 probability of not winning anything

Question 393667: For a fair game what should be the charge to play if there is a .003 probability to win $1,000, .007 probability to win $100, and .99 probability of not winning anything
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For a fair game what should be the charge to play if there is a .003 probability to win $1,000, .007 probability to win $100, and .99 probability of not winning anything
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Let the charge be "x".
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Winning values are: 1000-x ; 100-x ; -x
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Note: A fair game has an expected value of zero.
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Equation:
0.003(1000-x)+0.007(100-x)+0.99(-x) = 0
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3(1000-x) + 7(100-x) - 990x = 0
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3000-3x + 700-7x - 990x = 0
-1000x = -3700
x = $3.70 (amount you should pay to play the game)
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Cheers,
Stan H.
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