SOLUTION: if roulette were fair, how much should the house pay a player who bets $20 on a single number and it comes up? the odds against winning are 36:1

Question 268505: if roulette were fair, how much should the house pay a player who bets $20 on a single number and it comes up? the odds against winning are 36:1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if roulette were fair, how much should the house pay a player who bets $20 on a single number and it comes up? the odds against winning are 36:1
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P(losing) = 36/37
P(winning) = 1/37
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Let "x" be the amount the house pays.
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Note: Expected pay is zero if the game is "fair".
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E(x) = (winnings)P(win) + (loss)P(lose)
E(x) = (x-20)(1/37) + (-20)(36/37) = 0
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Multiply thru by 37 and solve for "x":
x-20 -20(36) = 0
x = 20*36+20
x = $740
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Cheers,
Stan H.
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