FRM Part I · FRM Exam Part I · Fundamentals of Probability
In a loan portfolio, 5% of borrowers default within a year. Of the defaulting borrowers, 80% had been flagged by an early-warning model. Of the non-defaulting borrowers, 10% were also flagged. A borrower is flagged. What is the probability, to the nearest percent, that the borrower defaults?
The probability is about 30%. By Bayes' rule, P(flag and default) = 0.04 and P(flag) = 0.04 + 0.095 = 0.135, giving 0.04/0.135 = 29.6%. The 80% figure is the reverse conditional probability, not the one asked for.
- A30%Correct
- B80%
- C4%
- D46%
Explanation
P(flag) = 0.05 x 0.80 + 0.95 x 0.10 = 0.04 + 0.095 = 0.135. P(default | flag) = 0.04 / 0.135 = 0.296, about 30%. Answering 80% confuses P(flag | default) with P(default | flag).
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