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

Which statement about events A and B, each with positive probability, is correct?

Mutually exclusive events with positive probabilities cannot be independent. Exclusivity makes the joint probability zero, while independence requires the joint probability to equal the product of two positive probabilities. Occurrence of one event tells you the other did not happen, which is dependence.

  1. AIf A and B are mutually exclusive, they must be independent
  2. BIf A and B are mutually exclusive, they cannot be independentCorrect
  3. CIf A and B are independent, they must be mutually exclusive
  4. DIf A and B are exhaustive, they must be mutually exclusive

Explanation

If A and B are mutually exclusive, P(A and B) = 0, but independence would require P(A)P(B) > 0, so they cannot be independent. Independent events with positive probabilities have a positive joint probability, so they are not mutually exclusive. Exhaustive events can overlap, for example A = return above 0 and B = return below 5%.

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