🟢 Bayes' Theorem — Round 2 (Repetition)
Can you still do this without looking? Try it:
"0.5% of transactions are fraudulent. A fraud detector has 99% sensitivity and 3% false positive rate. A transaction is flagged. What's the probability it's actually fraud?"
Work it out before reading the answer.
Answer:
P(Fraud|Flagged) = (0.99 × 0.005) / (0.99 × 0.005 + 0.03 × 0.995)
= 0.00495 / (0.00495 + 0.02985)
= 0.00495 / 0.0348
≈ 14.2%Even with 99% sensitivity, most flags are false positives because fraud is rare.