Both hit the target — Probability Aptitude Question
Both hit the target: Two marksmen hit a target with probabilities 3/5 and 2/3. What is the probability that both… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
Two marksmen hit a target with probabilities 3/5 and 2/3. What is the probability that both hit it?
Options
- 2/5
- 1/3
- 3/5
- 4/5
Show the answer and the worked solution
Correct answer: A. 2/5
Worked solution
- P(both) = 3/5 × 2/3 = 6/15 = 2/5.
Answer: 2/5.
The idea
Multiply for 'and' with independent events, add (minus the overlap) for 'or'. Cancel before multiplying to keep the fractions small.
Shortcut. 'Both' can never be likelier than either marksman alone, so 3/5 and 4/5 go at once; cancelling the 3s in 3/5 × 2/3 leaves 2/5.
Common trap. "3/5" — taking the weaker marksman's probability as the chance both hit, as if one hitting guaranteed the other; independent events multiply, 3/5 × 2/3 = 2/5.