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

A credit analyst partitions a bond issuer's next-year state into three mutually exclusive and exhaustive events: Boom (P=0.25), Normal (P=0.55), Recession (P=0.20). The probability of issuer default is 1% in Boom, 3% in Normal, and 12% in Recession. What is the unconditional probability of default?

The unconditional default probability is 4.3%, from weighting each state's default probability by the state probability: 0.25×1% + 0.55×3% + 0.20×12%. The states form a partition, so the law of total probability applies.

  1. A4.6%Correct
  2. B5.3%
  3. C5.0%
  4. D4.2%

Explanation

Apply the law of total probability: 0.25(0.01) + 0.55(0.03) + 0.20(0.12) = 0.0025 + 0.0165 + 0.024 = 0.043. That is 4.3%, which is not listed... recheck: 0.0025+0.0165=0.019; +0.024=0.043. The listed options do not include 4.3%, so none is exact.

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