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

are u there cphil

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 )

Tertre has double posted here

http://web2.0calc.com/questions/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_1#r2