One three rolls of a single die, you will lose $14 if a 6 turns up at least once, and you will win $6 otherwise. what is the expected value of the game?

The probability against a 6 turning up is (5/6)^3, or 0.5787037037037037037037037037037. So, the probability of at least one 6 rolled is 1-0.5787037037037037037037037037037=0.4212963. So:
5787037037037037037037037037037 x 6=3.4722222222222222222222222222222
0.4212963 x -14=-5.8981481481481481481481481481481
So, the expected value is 3.4722222222222222222222222222222
-5.8981481481481481481481481481481=$-2.426, or a loss of $2.43
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