Box I has 2 white and 3 black balls; box II has 4 white and 1 black. A box is picked at random and the ball drawn from it is white. What is the probability that it came from box II?

Explanation

1. 01

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

2. 02

   $P(\text{II} \mid W) = \frac{\frac{1}{2} \times \frac{4}{5}}{\frac{3}{5}} = \frac{2}{3}$.