Ana is a much better shot than Bruno. But once we know that exactly one of them hit the target, comparing their original percentages is no longer enough.
A Single Hit
Riddle statement
Ana and Bruno each fire one shot at the same target. The two shots are independent.
- Ana hits the target 75% of the time.
- Bruno hits it 25% of the time.
After both shots, we observe that exactly one of the two shots hit the target.
What is the probability that Ana made the hit?
Show solution
Solution
Only two scenarios are compatible with observing exactly one hit.
1. Ana hits and Bruno misses
The probability is:
(3/4) × (3/4) = 9/16.
2. Ana misses and Bruno hits
The probability is:
(1/4) × (1/4) = 1/16.
Once we know that one of these two cases occurred, their relative probabilities are 9 and 1. Therefore:
9 ÷ (9 + 1) = 9/10 = 90%.