CA Foundation · Quantitative Aptitude · Probability
Events A and B are independent with P(A) = 1/3 and P(B) = 1/4. What is the probability that exactly one of the two events occurs?
The probability is 5/12. Exactly one event occurs when A happens without B, giving (1/3)(3/4) = 3/12, or B happens without A, giving (2/3)(1/4) = 2/12. Adding these mutually exclusive cases gives 5/12, which excludes the case where both occur.
- A7/12
- B1/12
- C5/12Correct
- D1/2
Explanation
Exactly one occurs means A and not B, or B and not A. P = (1/3)(3/4) + (2/3)(1/4) = 3/12 + 2/12 = 5/12. The value 7/12 is P(A or B) and 1/12 is P(both).
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