CA Foundation · Quantitative Aptitude · Probability
A, B and C independently try to solve a problem with probabilities 1/2, 1/3 and 1/4 respectively. What is the probability that exactly two of them solve it?
The probability that exactly two solve it is 1/4. Adding the three mutually exclusive cases, AB only (3/24), AC only (2/24) and BC only (1/24), gives 6/24, which equals 1/4.
- A1/4Correct
- B1/24
- C11/24
- D1/6
Explanation
Exactly two means one of: A and B only = (1/2)(1/3)(3/4) = 3/24; A and C only = (1/2)(2/3)(1/4) = 2/24; B and C only = (1/2)(1/3)(1/4) = 1/24. Sum = 6/24 = 1/4. The value 1/24 counts only one of the three cases.
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