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 Three b***s are numbered 1, 2, 3 and placed in a bag. A ball is chosen, its number recorded, then the ball placed back in the bag. This proc

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Three b***s are numbered 1, 2, 3 and placed in a bag. A ball is chosen, its number recorded, then the ball placed back in the bag. This process is repeated twice more. The resulting 3 recorded numbers are added. Bob walks in the room after the three numbers have been recorded and is told only that the sum of the numbers is 6. Bob announces, "Oh, then they must all have been 2's." What is the probability that Bob is correct?

 Apr 8, 2015

Best Answer 

 #1
avatar+118723 
+7

Well the only possibilities are   2,2,2,  or  1,2,3

BUT  there is only one way to get 2,2,2

there are 3! = 6 ways of getting 1,2,3

that is

1,2,3

1,3,2

2,1,3

2,3,1

3,1,2

3,2,1

SO

the probability that the draw was 2,2,2  is     $${\frac{{\mathtt{1}}}{{\mathtt{7}}}}$$

 Apr 9, 2015

1+0 Answers

 #1
avatar+118723 
+7
Best Answer

Well the only possibilities are   2,2,2,  or  1,2,3

BUT  there is only one way to get 2,2,2

there are 3! = 6 ways of getting 1,2,3

that is

1,2,3

1,3,2

2,1,3

2,3,1

3,1,2

3,2,1

SO

the probability that the draw was 2,2,2  is     $${\frac{{\mathtt{1}}}{{\mathtt{7}}}}$$

Melody Apr 9, 2015

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