Solved by at least one of them — Aptitude Question
Solved by at least one of them: A can solve a problem with probability 2/3 and B with probability 3/4, independently. Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
A can solve a problem with probability 2/3 and B with probability 3/4, independently. What is the probability that the problem is solved?
Options
- 1/2
- 5/12
- 11/12
- 3/4
Show the answer and the worked solution
Correct answer: C. 11/12
Worked solution
- P(A fails) = 1/3, P(B fails) = 1/4; independent, so P(both fail) = 1/12.
- P(solved) = 1 − 1/12 = 11/12.
Answer: 11/12.
The idea
For independent events, P(at least one) = 1 − product of the failure probabilities. Complements turn 'or' questions into one multiplication.
Shortcut. Solved by at least one must beat the better solver's 3/4 alone, and only 11/12 does.
Common trap. 1/2 — multiplying the two success chances (2/3 × 3/4), which is the chance both solve it; one solver is enough.