FRM Part I · FRM Exam Part I · Fundamentals of Probability
A credit portfolio has 2% of loans in default. A screening model flags 90% of defaulted loans and also flags 8% of non-defaulted loans. Given that a randomly selected loan is flagged, what is the probability that it is in default (nearest value)?
The probability of default given a flag is about 18.7%. The total flag probability is 0.0964, made of 0.018 from defaulters and 0.0784 from non-defaulters. Dividing 0.018 by 0.0964 gives 0.1867. The low base rate of default dilutes the model's accuracy.
- A18.7%Correct
- B90.0%
- C2.0%
- D1.8%
Explanation
P(flag) = 0.02×0.90 + 0.98×0.08 = 0.018 + 0.0784 = 0.0964. By Bayes, P(default | flag) = 0.018 / 0.0964 = 0.1867, about 18.7%. The 1.8% option is the joint probability, not conditioned on the flag.
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