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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
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 #1
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are u there cphil

tertre  Sep 17, 2016
 #2
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Hi Tertre     laugh

 

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

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