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?

tertre
Sep 17, 2016

#2**0 **

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 )

Melody
Sep 18, 2016