A die is thrown. If it shows 1 or 2, a ball is drawn from bag A (3 red, 2 white); otherwise from bag B (1 red, 4 white). The ball drawn is red. What is the probability that it came from bag A?

Explanation

1. 01

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

2. 02

   $P(A \mid R) = \frac{\frac{1}{3} \times \frac{3}{5}}{\frac{1}{3}} = \frac{3}{5}$.