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An urn has 3 blue balls 4 red balls. 3 balls are drawn without replacement. find the probability of drawing 2 blue and 1 red given at least 1 blue is drawn

 Feb 6, 2020
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The possibilities that contain at least one blue ball are:

 

blue - blue - blue     (3/7) x (2/6) x (1/5)  =  1/35

 

blue - blue - red      (3/7) x (2/6) x (4/5)  =  4/35

blue - red - blue      (3/7) x (4/6) x (2/5)  =  4/35

red - blue - blue      (4/7) x (3/6) x (2/5)  =  4/35

 

blue - red - red       (3/7) x (4/6) x (3/5)  =  6/35 

red - blue - red       (4/7) x (3/6) x (3/5)  =  6/35

red - red - blue       (4/7) x (3/6) x (3/5)  =  6/35

 

1)  The sum of all the probabilities that have exactely two blue balls is:  12/35.

2)  The sum of all the probabilities that have at least one blue ball is:     31/35.

 

Dividing the result of 1) by the result of 2) gives:  (12/35) / (31/35)  =  12/31.

 Feb 6, 2020

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