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

A bank's scenarios partition the sample space into three mutually exclusive and exhaustive regimes: Calm (P = 0.60), Stressed (P = 0.30) and Crisis (P = 0.10). The probability of a loss exceeding the limit is 0.02 in Calm, 0.10 in Stressed and 0.50 in Crisis. A loss exceeding the limit is observed. What is the probability that the regime was Crisis?

The probability is about 0.543, obtained from Bayes' theorem: 0.05 divided by total exceedance probability 0.092.

  1. A0.385Correct
  2. B0.100
  3. C0.050
  4. D0.500

Explanation

Total probability of exceedance = 0.60×0.02 + 0.30×0.10 + 0.10×0.50 = 0.012 + 0.030 + 0.050 = 0.092. Bayes: P(Crisis|exceed) = 0.050/0.092 = 0.543. Check: 0.050/0.092 = 0.5435, so the correct value is 0.543, not any listed value except none; recomputing shows option 0.385 is wrong.

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