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A gambler rolls two dice and if he gets the same number on the both dice,...

A gambler rolls two dice and if he gets the same number on the both dice, he wins $10, and if he gets one die is double of the other die, he wins $20 . The cost of to play the game is $5. What is the expectation of this game?

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Answer #1

Let A=same number on the both dice={ (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) }

B=gets one die is double of the other die ={ (1,2), (2,4), (3,6), (2,1), (4,2),(6,3) }

n(S) = 36.

P(A) = 6/36 = 1/6

P(B)= 6/36 = 1/6

expectation of this game =(10-5)*(1/6)+(20-5)*(1/6)+(0-5)*(4/6)= 0

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