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

A bank's fraud model flags a transaction as suspicious. Historically, 2% of transactions are fraudulent. The model flags 90% of fraudulent transactions and also flags 5% of legitimate transactions. Given that a transaction is flagged, what is the probability that it is fraudulent (closest value)?

The probability is about 26.8%. The joint probability of fraud and a flag is 0.018, while the total probability of a flag is 0.067. Dividing gives roughly 27%. The 90% detection rate is not the answer because it is conditioned on fraud, not on being flagged.

  1. A26.8%Correct
  2. B18.0%
  3. C90.0%
  4. D2.0%

Explanation

P(F)=0.02, P(flag|F)=0.90, P(flag|not F)=0.05. P(flag)=0.02*0.90+0.98*0.05=0.018+0.049=0.067. P(F|flag)=0.018/0.067=26.9%, closest to 26.8%. The 18.0% option is the joint probability times 1000 misread, and 90% confuses P(flag|F) with P(F|flag).

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