A die is thrown. If it shows 1, a ball is drawn from urn I (2 white, 3 black); if it shows 2 or 3, from urn II (4 white, 1 black); otherwise from urn III (3 white, 2 black). What is the probability that the ball is white?

Explanation

1. 01

   $P(\text{I}) = \frac{1}{6}$, $P(\text{II}) = \frac{2}{6}$ and $P(\text{III}) = \frac{3}{6}$.

2. 02

   $P(W) = \frac{1}{6} \times \frac{2}{5} + \frac{2}{6} \times \frac{4}{5} + \frac{3}{6} \times \frac{3}{5} = \frac{2 + 8 + 9}{30} = \frac{19}{30}$.