Bin A has one white ball and four black b***s. Bin B has three b***s labeled $1 and one ball labeled $7 . Bin W has five b***s 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?
Hi Tertre
Bin A has one white ball and four black b***s.
Bin B has three b***s labeled $1 and one ball labeled $7 .
Bin W has five b***s 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?
I am not very familiar with expected wins but this is what seems sensible to me.
If you choose a ball from bin B then the average win would be (3*1+7)/ 4 = $2.50
If you choose a ball from bin W then the average win would be (5*8+500)/6 = $90
so the answer would be (4/5 * $2.50) + ( 1/5 * $90) = $2 + $18 = $20
I would expect to win $20
( The expected win is the average win you would get if you played the same game an infinite number of times )