In the gambling game chuck-a-luck, for a $1 bet it is possible to win $1, $2, or $3 with respective probabilities 75/216, 15/216, and 1/216. One dollar is lost with probability 125/216. Let X equal the payoff for this game and find E(X). Note that when a bet is won, the $1 that was bet, in addition to the $1, $2, or $3 that is won, is returned to the bettor.

Solution :

Step 1 of 2:

Here in a gambling game for a $1 bet it is possible to win $1, $2, and $3 with probabilities 75/2716, 15/216,1/216 respectively. On dollar can lost with probability 125/216. When a bet is won for $1 then it will add to the amount $1,$2, or $3 that is one , and it will return to the bettor.If X defined the payoff for this game then we have to find the expected payoff for the game E(x).