Question 218974: If a gambler rolls two dice and gets a sum of 9, he wins $20, and if he gets a sum of 3, he wins $40. The cost to play the game is $5. What is the expectation (to the nearest cent) of this game?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If a gambler rolls two dice and gets a sum of 9, he wins $20, and if he gets a sum of 3, he wins $40. The cost to play the game is $5. What is the expectation (to the nearest cent) of this game?
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Let the random variable "x" be a count of gain for the gambler.
X = 15, 35, -5
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Sum of 9: (3,6),(4,5),(5,4)(6,3)
P(sum of 9) = 4/36
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Sum of 3: (1,2),(2,1)
P(sum of 3) = 2/36
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E(X) = 15(4/36) + 35(2/36)+(-5)(30/36)
E(X) = [60 + 70 -150]/36 = -56 cents
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Cheers,
Stan H.
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