In a quiz, three contestants answer the same question independently; the probabilities that they answer it correctly are $\frac{4}{5}$, $\frac{1}{2}$ and $\frac{1}{4}$. What is the probability that exactly one of them answers it correctly?

Explanation

1. 01

   Only the first: $\frac{4}{5} \times \frac{1}{2} \times \frac{3}{4} = \frac{12}{40}$; only the second: $\frac{1}{5} \times \frac{1}{2} \times \frac{3}{4} = \frac{3}{40}$; only the third: $\frac{1}{5} \times \frac{1}{2} \times \frac{1}{4} = \frac{1}{40}$.

2. 02

   $\frac{12 + 3 + 1}{40} = \frac{16}{40} = \frac{2}{5}$.