Bag I has 4 white and 2 black balls; bag II has 2 white and 4 black balls. Two balls are drawn at random from bag I and put into bag II. A ball is then drawn at random from bag II. What is the probability that it is white?

Explanation

1. 01

   The two balls moved are both white, one of each, or both black, with probabilities $\frac{6}{15}$, $\frac{8}{15}$ and $\frac{1}{15}$; bag II then holds 4, 3 or 2 white balls of 8.

2. 02

   $\frac{6}{15} \times \frac{4}{8} + \frac{8}{15} \times \frac{3}{8} + \frac{1}{15} \times \frac{2}{8} = \frac{24 + 24 + 2}{120} = \frac{5}{12}$.