SOLUTION: We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value

Question 276086: We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value for the game?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value for the game?
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Random "Values" to the player: -30 , 2, 3, 4, 5, 6 , 8, 9, 10, 11, 12
P(get sum of 2) = 1/36
P(get sum of 3) = 2/36
P(get sum of 4) = 3/36
P(get sum of 5) = 4/36
P(get sum of 6) = 5/36
P(get sum of 7) = 6/36
P(get sum of 8) = 5/36
P(get sum of 9) = 4/36
P(get sum of 10)= 3/36
P(get sum of 11) = 2/36
P(get sum of 12) + 1/36
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Procedure:
E(x) = (2+12)(1/36) + (3+11)(2/36) + (4+10)(3/36) + (5+9)(4/36) + (6+8)(5/36)
-30(6/36)
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E(x) = (14/36)[(1+2+3+4+5)]-30(6/36)] = (7/18)(15)-5 = +83 cents
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Cheers,
Stan H.

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