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CA Foundation · Quantitative Aptitude · Probability

For two events A and B of a sample space, P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. What is the probability that neither A nor B occurs?

The probability is 0.3. First find P(A or B) using the addition theorem: 0.5 plus 0.4 minus 0.2 gives 0.7. The chance that neither event happens is the complement of this, which is 1 minus 0.7, equal to 0.3.

  1. A0.3Correct
  2. B0.7
  3. C0.1
  4. D0.2

Explanation

By the addition theorem, P(A or B) = 0.5 + 0.4 - 0.2 = 0.7. The probability that neither occurs is 1 - 0.7 = 0.3. The value 0.1 comes from wrongly ignoring the overlap, and 0.7 is the probability of at least one event.

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