Neither passes — Probability Aptitude Question
Neither passes: Two students have probabilities 0.6 and 0.7 of passing an exam, independently. Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 55 seconds
Question
Two students have probabilities 0.6 and 0.7 of passing an exam, independently. What is the probability that neither passes?
Options
- 0.12
- 0.18
- 0.28
- 0.42
Show the answer and the worked solution
Correct answer: A. 0.12
Worked solution
- P(both fail) = 0.4 × 0.3 = 0.12.
Answer: 0.12.
The idea
For independent events, multiply the individual probabilities. 'Neither' means both fail, so use the failure probabilities.
Shortcut. Turn each pass chance into a fail chance (0.4 and 0.3) and multiply: 0.12. Check: at least one passes = 0.6 + 0.7 − 0.42 = 0.88 = 1 − 0.12.
Common trap. "0.42" — multiplying the pass chances 0.6 × 0.7, which is the probability that both pass.