Two archers shoot at a target independently, hitting it with probabilities 0.6 and 0.3. Each shoots once, and the target is hit exactly once. What is the probability that the first archer hit it?

Explanation

1. 01

   Only the first hits: $0.6 \times 0.7 = 0.42$; only the second: $0.4 \times 0.3 = 0.12$; so exactly one hit has probability $0.54$.

2. 02

   $\frac{0.42}{0.54} = \frac{7}{9}$.