Two machines in a factory work independently. On a given day, machine X breaks down with probability $\frac{1}{5}$ and machine Y with probability $\frac{1}{4}$. What is the probability that exactly one of the two machines breaks down that day?

Explanation

1. 01

   Exactly one = (X fails and Y works) or (X works and Y fails).

2. 02

   $\frac{1}{5} \times \frac{3}{4} = \frac{3}{20}$ and $\frac{4}{5} \times \frac{1}{4} = \frac{4}{20}$.

3. 03

   These cases cannot both happen, so add: $\frac{7}{20}$.