Positive doesn’t mean certain.
A test that's 99% accurate can still be wrong more often than right, if the thing it's testing for is rare enough. At 1% prevalence, a 99%-accurate test throws up one false alarm for every real case it catches — a coin flip, from a "99% accurate" test. That's Bayes' theorem, and the base-rate fallacy is why it feels wrong.
P(D|+)
=
P(+|D)P(D)
P(+)
P(+) = P(+|D)P(D) + (1−P(−|¬D))(1−P(D))
has disease · tests positive
no disease · tests positive (false alarm)
has disease · tests negative (missed)
no disease · tests negative
Prevalence D
P(D)
0.01%log scale — rare diseases span orders of magnitude20%
Sensitivity +|D
P(+|D)
80%catches this share of real cases100%
Specificity −|¬D
P(−|¬D)
80%clears this share of the healthy100%
P(disease | positive test)
%
Try
This is Bayes' theorem, applied to medical testing. P(+) — the overall chance of a positive result — is expanded via the law of total probability into true positives plus false positives. The gap between "P(disease | positive test)" and the test's own accuracy is the base-rate fallacy: intuition tracks the test's accuracy and ignores how rare the disease is, but when a condition is rare, most positives come from the much larger healthy population's small error rate, not from the small diseased population's high catch rate. This is exactly why a single positive screening test — a mammogram, an HIV screen — is normally followed by a second, different, confirmatory test rather than treated as a diagnosis on its own. The mammography-style preset uses illustrative, rounded figures (prevalence ≈1%, sensitivity ≈90%, specificity ≈91%) meant to carry the shape of the argument, not real clinical statistics for any specific screening program — this page is for pedagogy, not medical guidance.