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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

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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?

Sep 17, 2016

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are u there cphil

Sep 17, 2016
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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 )

Sep 18, 2016