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.