Probability · Bayes with a census

A thousand people, one test

Prior, sensitivity, false positives — counted as people, then as a posterior. The base-rate trap, made visible.

Prevalence P(D)1%Sensitivity P(+ | D)90%False positive P(+ | ¬D)5%

A thousand people walk through the clinic. The posterior is not the sensitivity. It is true positives divided by everyone who tested positive — including the healthy majority who still trigger the test.

The thousand

Sick 10Healthy 990

Among the sick

True + 9False − 1

Among the healthy

False + 50True − 941

P(D | +)

15.4%

9 true positives / 59 positive tests