Only one of 5 keys opens a lock. The keys are tried one at a time in a random order, and a key that fails is set aside. What is the probability that the lock opens within the first three tries?

Explanation

1. 01

   The lock stays shut through three tries with probability $\frac{4}{5} \times \frac{3}{4} \times \frac{2}{3} = \frac{2}{5}$.

2. 02

   So it opens within three tries with probability $1 - \frac{2}{5} = \frac{3}{5}$.