CA Foundation · Quantitative Aptitude · Probability
For two events A and B, P(A) = 0.45, P(B) = 0.35 and P(A ∪ B) = 0.65. What is the probability that neither A nor B occurs?
The probability that neither event occurs is 0.35. The union probability 0.65 covers all cases where at least one event happens, so the complement, 1 minus 0.65, gives the chance that neither happens.
- A0.45
- B0.20
- C0.35Correct
- D0.55
Explanation
P(A ∪ B) = 0.65 is the probability that at least one occurs, so neither occurs with probability 1 - 0.65 = 0.35. Option 0.55 wrongly uses 1 - P(A) = 0.55, and 0.20 is P(A ∩ B) = 0.45 + 0.35 - 0.65 = 0.15 mistaken, not the required quantity.
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