Bin $A$ has one white ball and four black balls. Bin $B$ has three balls labeled $\$1$ and one ball labeled $\$7$. Bin $W$ has five balls labeled $\$8$ and one ball labeled $\$500$. A game is played as follows: a ball is randomly selected from bin $A$. If it is black, then a ball is randomly selected from bin $B$; otherwise, if the original ball is white, then a ball is randomly selected from bin $W$. You win the amount printed on the second ball selected. What is your expected win

$20

Step-by-step explanation:

Bin A:                             Bin B:                  Bin W:

white ball: 20%              $1: 75%                $8: 5/6

black ball: 80%              $7: 25%               $500: 1/6

first we can calculate the expected return of bins B and W:

expected return if the ball is black = ($1 x 75%) + ($7 x 25%) = $2.50

expected return if the ball is white = ($8 x 5/6) + ($500 x 1/6) = $90

expected return of the game = (expected return of a black ball x probability of choosing a black ball) + (expected return of a white ball x probability of choosing a white ball) =($2.50 x 80%) + ($90 x 20%) = $2 + $18 = $20

step-by-step explanation:

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