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 will win?

Answer 1

There are 2 chances out of 6 to win $3

Every 6 rolls you are expected to win $6

Every 3 rolls you are expected to win $3.

On average, even though it's impossible, every roll you would make $1.