In the gambling game chuck-a-luck, for a $1bet it is possible to win $1, $2, or $3 with respective probabilities 75/216,15/216,and1/216. 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.

Step-by-step explanation:

Given:

Probability of winning $1, P($1) =

Probability of winning $2, P($2) =

Probability of winning $3, P($3) =

Probability of losing $1, P(-$1) =

Now,

Expected return = ∑ ( X × (PX) )

here, X is the payoff and, P(X) is the probability of winning

the losing amount is depicted with the negative payoff

Thus,

expected return = $1 × P($1) + $2 × P($2) + $3 × P($3) + (-$1) × P(-$1)

or

expected return =  +    +  -

or

expected return =  

or

expected return =