Question

A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out form the latter. Find the probability that the ball drawn is white.

Answer 1

Given:

Bag I contains 4 white and 5 black balls.

Bag II contains 3 white and 4 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

Let E₃ denote the event that white ball is drawn from bag II.

Hence, we 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 \(\cfrac{83}{150}.\)