Three bags hold 5 balls each: bag I has 2 white, bag II has 3 white and bag III has 4 white, the rest being black. A bag is picked at random and a ball drawn from it is white. What is the probability that it came from bag III?

Explanation

1. 01

   $P(W) = \frac{1}{3}\left(\frac{2}{5} + \frac{3}{5} + \frac{4}{5}\right) = \frac{3}{5}$.

2. 02

   $P(\text{III} \mid W) = \frac{\frac{1}{3} \times \frac{4}{5}}{\frac{3}{5}} = \frac{4}{9}$.