Box I has 3 red and 7 white balls; box II has 6 red and 4 white balls. A box is picked at random and a ball drawn from it is red. What is the probability that it came from box I?

Explanation

1. 01

   $P(R) = \frac{1}{2} \times \frac{3}{10} + \frac{1}{2} \times \frac{6}{10} = \frac{9}{20}$.

2. 02

   $P(\text{I} \mid R) = \frac{3/20}{9/20} = \frac{1}{3}$.