Bag I has 3 red and 4 black balls; bag II has 5 red and 4 black. A bag is picked at random and the ball drawn from it is red. What is the probability that it came from bag II?

Explanation

1. 01

   $P(\text{II} \mid R) = \frac{P(\text{II})P(R \mid \text{II})}{P(R)} = \frac{\frac{1}{2} \cdot \frac{5}{9}}{\frac{31}{63}}$.

2. 02

   $\frac{5}{18} \times \frac{63}{31} = \frac{35}{62}$.