Bag I has 3 red and 2 blue balls; bag II has 3 red and 1 blue ball. A bag is picked at random and two balls are drawn from it, one after the other, without replacement. What is the probability that both are red?

Explanation

1. 01

   Both red from bag I: $\frac{3}{5} \times \frac{2}{4} = \frac{3}{10}$; from bag II: $\frac{3}{4} \times \frac{2}{3} = \frac{1}{2}$.

2. 02

   $\frac{1}{2} \times \frac{3}{10} + \frac{1}{2} \times \frac{1}{2} = \frac{3}{20} + \frac{5}{20} = \frac{2}{5}$.