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

A bank's fraud model flags 5% of all transactions. Of flagged transactions, 40% are actually fraudulent. Of unflagged transactions, 1% are fraudulent. What is the overall (unconditional) probability that a randomly selected transaction is fraudulent?

The unconditional fraud probability is 2.95%. Weight each branch by its probability: flagged contributes 5% x 40% = 2.00%, and unflagged contributes 95% x 1% = 0.95%. Adding both gives 2.95%. Omitting either branch gives a wrong figure.

  1. A2.95%Correct
  2. B4.00%
  3. C2.00%
  4. D0.95%

Explanation

Use the law of total probability: P(F) = 0.05 x 0.40 + 0.95 x 0.01 = 0.020 + 0.0095 = 0.0295, or 2.95%. Choosing 2.00% ignores the fraud among unflagged transactions. Choosing 0.95% ignores the flagged contribution.

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