the base-rate fallacy
The base-rate fallacy is the mistake of judging how probable something is from the evidence alone, while ignoring how rare or common it was to begin with. Told that a test is '99% accurate' and that yours came back positive, most people leap to '99% chance I have it'. That feels right and is badly wrong, because it throws away the base rate — the prior prevalence of the disease in the population.
Here is why a rare condition with an accurate test still yields mostly false positives. Imagine 10000 people where the disease afflicts 1 in 1000, so 10 are truly sick and 9990 are healthy. A 99%-accurate test correctly flags about 10 of the sick. But its 1% false-positive rate flags about 1% of 9990 healthy people, which is roughly 100 people. So about 110 test positive, but only 10 are actually sick. Your chance of disease given a positive is about 10 out of 110, under 10% — not 99%. The healthy majority is so large that even a tiny error rate produces a flood of false alarms that swamps the few true cases.
This is not a quirk of medicine; it is everywhere there is screening for something rare: airport threat detection, fraud alerts, rare-event predictions, DNA database matches. The fix is always the same: run it through Bayes' theorem and respect the prior. The deep reason the intuition fails is the confusion of P(positive given sick), which the test guarantees, with P(sick given positive), which is what you care about — and the two diverge wildly when the base rate is low.
Of 10000 people with prevalence 0.1%: 10 sick, 9990 healthy. A 99% test true-flags ~10 sick and false-flags ~100 healthy. Positives: ~110, of whom only 10 are sick. P(sick given positive) is about 9%, despite '99% accuracy'.
When the disease is rare, false positives from the huge healthy group outnumber true positives.
'Accuracy' usually quotes P(test correct given true state), which says nothing on its own about P(true state given test). Always demand the base rate before trusting a positive result.