CFA Level 1: Joint Probability of Events A and B | Answer and Explanation

Joint Probability of Events A and B

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Question

The joint probability of events A and B occurring equals 0.11. The probability of neither A nor B occurring equals 0.64. If P(A) equals 0.24, the probability of B occurring equals ________.

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A. B. C. D.

D

We are given that P(neither A nor B) = 0.64, P(A and B) = 0.11 and P(A) = 0.24. The probability of neither A nor B occurring equals one minus the probability of either A or B occurring i.e. P(neither A nor B) = 1 - P(A or B).

Thus, P(A or B) = 1 - P(neither A nor B) = 1 - 0.64 = 0.36.

Now, P(A or B) = P(A) + P(B) - P(A and B)

Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.36 - 0.24 + 0.11 = 0.23.

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