One bag contains 4 yellow and 5 red balls. Another bag contains 6 yellow and 3 red balls. A ball is transferred from the first bag to the second bag, and then a ball is drawn from the second bag. Find the probability that ball drawn is yellow.

Given:

The bag I contains 4 yellow and 5 red balls.

Bag II contains 6 yellow and 3 red 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 yellow ball from bag II –

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

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

Let E₁ be the event that yellow ball is drawn from the bag I and E₂ be the event that red ball is drawn from the bag I.

Now, we have

We also have

Let E₃ denote the event that yellow 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 yellow is.