Question

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. What is the expected amount you win?

Answer 1

On the presumption that it is a cubic die, on average you will not gain nor lose any money. Out of the six faces, 1/3 of them are a 5 or a 2. So 1/3 of the time, you will gain 3$, but will lose 1$ from the initial payment. 1/3 of 3$ is 1$, so on average, you will gain 1$, while losing 1$.
Another way of looking at it is to take the possible out comes, and add the gains/loses, and you will come up with 0$.
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