hard · FRM Part 1

A fraud detection algorithm has a prior probability of fraud on any transaction of 0.1%. The algorithm triggers a 'Level 1' alert with 80% sensitivity and 2% false-positive rate. Upon manual review, a 'Level 2' suspicious pattern is identified with 90% sensitivity and 5% false-positive rate. Assuming signals are conditionally independent, find the final probability of fraud.

1. 41.98%
2. 3.85%
3. 72.00%
4. 1.00%

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