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

A risk analyst classifies next quarter's outcomes for a loan portfolio into three events: A = 'default losses below 1%', B = 'default losses between 1% and 3%', and C = 'default losses above 3%'. Boundaries are assigned so that no outcome falls in two events. Which statement best describes A, B and C?

The events are mutually exclusive and collectively exhaustive, because every possible loss outcome falls into exactly one of the three ranges. No two can occur together, and together they cover all outcomes. Independence is a separate concept and does not apply here.

  1. AThey are mutually exclusive and collectively exhaustiveCorrect
  2. BThey are mutually exclusive but not collectively exhaustive
  3. CThey are collectively exhaustive but not mutually exclusive
  4. DThey are independent events

Explanation

Every possible loss level falls into exactly one of the three ranges, so no two events can occur together (mutually exclusive) and together they cover the whole sample space (exhaustive). Independence is a different property; mutually exclusive events with positive probability are in fact dependent.

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