Question

Two urns contain 5 black balls and 7 white balls and 3 black balls and 9 white balls respectively. One ball is transferred to the second urn and then one ball is drawn from the second urn.
What is the probability that the first ball transferred is white, given that the ball drawn is white?

• A.
• B.
• C.
• D.
• E. None of these

Answer 1

The correct option is D

P(A) = probability that the ball transferred from urn first to second is white
P(B) = probability that the ball drawn from second urn is black.

Case I: If white ball goes to urn II
P(C) = $\frac{5}{12}\times \frac{9}{13}$ = $\frac{45}{156}$

Case II: If black ball goes to urn II
P(D) = $\frac{7}{12}\times \frac{10}{13}$ = $\frac{70}{156}$

Thus, P(B) = P(C) + P(D) = $\frac{115}{156}$

P($\frac{A}{B}$) = Probability of event A when B has occurred = Probability that ball drawn from II urn is black = $\frac{14}{23}$