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). What is the probability that the ball is red?

Explanation

1. 01

   $P(A) = \frac{2}{6} = \frac{1}{3}$, $P(B) = \frac{2}{3}$.

2. 02

   $P(R) = \frac{1}{3} \times \frac{3}{5} + \frac{2}{3} \times \frac{1}{5} = \frac{3 + 2}{15} = \frac{1}{3}$.