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?
Do I just find the expected value of Bin B and Bin W? Then I multiply 1/5 with the expected value of Bin B, and then 4/5 * the expected value of Bin W? I'm not really sure. It would be awesome if you could help.