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Bayes' theorem combines a prior with test performance: posterior = sensitivity x prior divided by the total probability of a positive result. The counter-intuitive consequence is that with a 1 percent prior, a 95 percent sensitive and 90 percent specific test still yields a posterior under 10 percent, because false positives from the large negative population swamp the true positives.
Bayes' theorem
P(D|+) = sens x prior / (sens x prior + (1 - spec) x (1 - prior)); LR+ = sens / (1 - spec)
Base rates dominate. At a 1 percent prior, out of 10,000 cases there are 95 true positives but around 990 false positives, so most positive results are wrong.
Identically for alerting and fraud. A rare-event detector with high accuracy still produces mostly false alarms, which is why precision at the operating point matters more than accuracy.