In the gambling game chuck-a-luck, for a $1 bet, it is possible to win $1, $2, or $3 with respective probabilities of 75/216, 15/216, and 1/216. One dollar is lost with a probability of 125/216. Let X equal the winnings for this game.
a.) Find E(X). (Note that when a bet is won, the $1 that was bet is returned to the bettor in addition to the $1, $2, or $3 that is won, but the returned dollar does not count as part of the winnings.)