Q10 of 249 Page 32

One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.

Given:


Bag I contains 4 white and 5 black balls.


Bag II contains 6 white and 7 black balls.


A ball is transferred from bag I to bag II and then a ball is drawn from bag II.


There are two mutually exclusive ways to draw a white ball from bag II –


a. A white ball is transferred from bag I to bag II, and then, a white ball is drawn from bag II


b. A black ball is transferred from bag I to bag II, and then, a white ball is drawn from bag II


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


Now, we have





We also have





Let E3 denote the event that white ball is drawn from bag II.


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 white is.


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