Q. 13.7( 3 Votes )

A bag A contains 5 white and 6 black balls. Another bag B contains 4 white and 3 black balls. A ball is transferred from bag A to the bag B, and then a ball is taken out of the second bag. Find the probability of this ball being black.

Answer :

Given:


Bag A contains 5 white and 6 black balls.


Bag B contains 4 white and 3 black balls.


A ball is transferred from bag A to bag B, and then a ball is drawn from bag B.


There are two mutually exclusive ways to draw a black ball from bag B –


a. A white ball is transferred from bag A to bag B, and then, a black ball is drawn from bag B


b. A black ball is transferred from bag A to bag B, and then, a black ball is drawn from bag B


Let E1 be the event that white ball is drawn from bag A and E2 be the event that black ball is drawn from bag A.


Now, we have





We also have





Let E3 denote the event that black ball is drawn from bag B.


Hence, we have





We also have





Using the theorem of total probability, we get


P(E3) = P(E1)P(E3|E1) + P(E2)P(E3|E2)





Thus, the probability of the drawn ball being black is.


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