Question

Two urns contain 3 white and 4 black balls, and 2 white and 5 black balls. one ball is transferred to the second urn and then one ball is drawn from the second urn. find the probability that the first ball transferred is black, given that the ball drawn is black.

Answer 1

Solution:

P(A) = probability that the ball transferred from urn first to second is black:
=

712
P(B) = probability that the ball drawn from second urn is black.

Case I: If white ball goes to urn II
P(C)=

512×913

Case II: If black ball goes to urn II
P(D)=

712×1013

Thus, P(B)=P(C)+P(D)=(

45156)+(70156)=115156

P(

AB)= Probability of event A when B has occurred
= Probability that ball drawn from II urn is black

⇒ 

P(A intersects B)P(B)=(712×1013)(115156) 
= 70/115 = 14/23