Coin A is fair; coin B has a head on both sides. One coin is picked at random and tossed, and it shows a head. What is the probability that it is coin B?

Explanation

1. 01

   $P(H) = \frac{1}{2} \times \frac{1}{2} + \frac{1}{2} \times 1 = \frac{3}{4}$.

2. 02

   $P(B \mid H) = \frac{1/2}{3/4} = \frac{2}{3}$.