The bag A contains 8 white and 7 black balls while the bag B contains 5 white and 4 black balls. One balls is randomly picked up from the bag A and mixed up with the balls in bag B. Then a ball is randomly drawn out from it. Find the probability that ball drawn is white.

Given:


Bag A contains 8 white and 7 black balls.


Bag B contains 5 white and 4 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 white ball from bag B –


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


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


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