SOLUTION: Please help me on this question. Two urns contain white and black balls. Urn 1 contains 3 white balls and 4 black balls. Urn 2 contains 5 white and 3 black balls. Blindfolded, y

Question 1183551: Please help me on this question.
Two urns contain white and black balls. Urn 1 contains 3 white balls and 4 black balls. Urn 2 contains 5 white and 3 black balls. Blindfolded, you draw a ball randomly from one of the two urns. The ball drawn is then put inside a third urn which contains 2 white and 3 black balls.
a) What is the probability of drawing a black ball from the third urn?
b) What is the probability that a black ball drawn from the third urn came from Urn 2?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
This is an easy application of the law of total probability and Bayes' theorem.

a) P(B) = P(B|(U1 and W))*P(W|U1)*P(U1) + P(B|(U1 and B))*P(B|U1)*P(U1) +
P(B|(U2 and W))*P(W|U2)*P(U2) + P(B|(U2 and B))*P(B|U2)*P(U2)
= 3/28 + 4/21 + 5/32 + 1/8 = , approximately 0.57887 to 5 d.p.
b) P(U2|B) = P(U2 and B)/P(B) = (9/32)/(389/672) = , approximately 0.48586 to 5 d.p.
RELATED QUESTIONS
Please help? Two urns contain each contain white balls and black balls. Urn 1 contains... (answered by fractalier,Fermat,AnlytcPhil)

Please help me on this question. Thanks! Two urns contain white and black balls. Urn 1... (answered by robertb)

Two urns contain 4 white and 6 black balls and 3 white and 8 black balls respectively. If (answered by greenestamps)

Two urns contain 4 white and 6 black balls and 3 white and 8 black balls respectively. If (answered by Boreal)

Two urns contain respectively 3 white, 7 red, 15 black balls and 10 white, 6 red, 9 black (answered by Fombitz)

Two urns each contain green balls and black balls. Urn 1 contains four green balls and... (answered by Simnepi)

There are 3 urns containing 2 white and 3 black balls, 3 white and 2 black balls and 4... (answered by richwmiller)

Two urns contain white balls and yellow balls. The first urn contains 2 white balls and 7 (answered by addingup)

Cud you help me solve this question An urn contains 9 blue, 7 white and 4 black balls. (answered by stanbon)