Answer :

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 E_{1} be the event that white ball is drawn from bag I and E_{2} be the event that black ball is drawn from bag I.

Now, we have

We also have

Let E_{3} 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(E_{3}) = P(E_{1})P(E_{3}|E_{1}) + P(E_{2})P(E_{3}|E_{2})

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

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