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FRM Part I · FRM Exam Part I · Fundamentals of Probability

Two events satisfy P(A) = 0.50, P(B) = 0.40 and P(A and B) = 0.30. Which of the following statements is correct?

A and B are positively dependent. P(A|B) = 0.30/0.40 = 0.75, higher than P(A) = 0.50. Independence would require a joint probability of 0.50 x 0.40 = 0.20, not 0.30. Mutually exclusive events would have a joint probability of zero.

  1. AA and B are independent because P(A and B) is positive
  2. BA and B are mutually exclusive because P(A and B) is positive
  3. CA and B are positively dependent because P(A|B) = 0.75 exceeds P(A)Correct
  4. DA and B are negatively dependent because P(B|A) = 0.60 exceeds P(B)

Explanation

P(A|B) = 0.30/0.40 = 0.75, which exceeds P(A) = 0.50, so the events are positively dependent. Independence would need a joint probability of 0.20. Mutually exclusive events have joint probability zero. Option D's P(B|A)=0.60 is right, but exceeding P(B) indicates positive, not negative, dependence.

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