# A bag contains 6 red and 8 black balls and another bag contains 8 red and 6 black balls. A ball is drawn from the first bag and without noticing its colour is put in the second bag. A ball is drawn from the second bag. Find the probability that the ball drawn is red in colour.

Given:

Bag I contains 6 red and 8 black balls.

Bag II contains 8 red and 6 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 red ball from bag II –

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

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

Let E1 be the event that red 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 red 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 red is.

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