SOLUTION: On two rolls of a single die, you will lose $10 if a 4 turns up at least once, and you will win $3 otherwise. What is the expected value of the game?

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Question 747801: On two rolls of a single die, you will lose $10 if a 4 turns up at least once, and you will win $3 otherwise. What is the expected value of the game?

Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!
The chance of a 4 is 1 in 6.
In the 36 possible combinations, 6 times a 4 will be first, and 6 times a 4 will be second, so 12 rolls out of 36. But one of these are double counted, the 4,4 outcome. So it's really 11 rolls that contain a 4. The remaining 25 outcomes contain no 4.
11 * -$10 = -$110
25 * $3 = $75
36 rolls produce -$35, or -$0.97 per roll.