You randomly select one of the urns: X, Y, or Z. You then randomly draw one ball out of the selected urn and note its color. The urn contain the following colored balls:
Urn X: 2 red, 3 white, and 2 blue.
Urn Y: 1 red, 1 white, 2blue
Urn Z: 1 red, 1 white, 2blue
1). If the ball is blue, what is the probability that it was drawn from Urn X____?
2.) If the ball is either blue or white, what is the probability that it was drawn from urn X____?

Question

You randomly select one of the urns: X, Y, or Z.  You then randomly draw one ball out of the selected urn and note its color.  The urn contain the following colored balls:
Urn X: 2 red, 3 white, and 2 blue.
Urn Y: 1 red, 1 white, 2blue
Urn Z: 1 red, 1 white, 2blue
1). If the ball is blue, what is the probability that it was drawn from Urn X____?
2.) If the ball is either blue or white, what is the probability that it was drawn from urn X____?

icecube · Answer

P(X/B)=probability of getting blue ball from urn X ,if the ball is blue .
P(X/B)= p(X∩B)/P(B) = (probability of getting blue ball from Urn X)/Total probability of      
                                                                                                     getting blue ball)
|dw:1329461606425:dw| 
therefore
       P(X/B) =(1/3*2/7)/(1/3*2/7+1/3*2/4+1/3*2/4)
                  =2/9