One card is lost from a well-shuffled pack of 52. A card is then drawn at random from the remaining 51. What is the probability that it is a heart?

Explanation

1. 01

   Split on the lost card: a heart with probability $\frac{13}{52}$, leaving 12 hearts; not a heart with probability $\frac{39}{52}$, leaving 13.

2. 02

   $\frac{13}{52} \times \frac{12}{51} + \frac{39}{52} \times \frac{13}{51} = \frac{156 + 507}{2652} = \frac{1}{4}$.