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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 (to the nearest 0.1%)?

The probability is about 26.9%. The total flag probability is 0.018 from fraud plus 0.049 from legitimate transactions, or 0.067. Dividing the fraud-and-flag probability of 0.018 by 0.067 gives 26.9%, because most flags come from the much larger legitimate group.

  1. A26.9%Correct
  2. B18.0%
  3. C90.0%
  4. D2.0%

Explanation

P(flag) = 0.02*0.90 + 0.98*0.05 = 0.018 + 0.049 = 0.067. P(fraud|flag) = 0.018/0.067 = 26.9%. The 18.0% option is the joint probability expressed as a percentage, which fails to divide by P(flag).

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