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

A risk analyst defines two events for next quarter: A = 'the portfolio loses more than 5%' and B = 'the portfolio gains more than 2%'. Which statement about A and B is correct?

The events are mutually exclusive, because a quarterly loss above 5% and a gain above 2% cannot occur together. They are not exhaustive, since returns between -5% and +2% fall outside both, and they are not independent because one occurring rules out the other.

  1. AThey are mutually exclusive, because both cannot occur in the same quarterCorrect
  2. BThey are independent, because their outcomes have no common cause
  3. CThey are exhaustive, because one of them must occur
  4. DThey are complementary, because P(A) + P(B) equals 1

Explanation

A loss above 5% and a gain above 2% cannot both happen over the same quarter, so the intersection is empty and the events are mutually exclusive. They are not exhaustive because returns between -5% and +2% fall in neither event. Mutually exclusive events with positive probabilities are dependent, not independent, and nothing forces their probabilities to sum to 1.

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