# 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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