Conditional probability and Bayes' theorem: disease testing

MathematicsProbabilityAges 17–18

A medical-testing problem: disease prevalence, sensitivity P(+|disease), and specificity P(−|healthy) are given. A tree diagram, a 2×2 table for N people, and a grid of 1000 colored dots show why the true probability of having the disease given a positive test, P(disease|+), is often much lower than the sensitivity; drag the sliders to watch the total probability formula and Bayes' theorem change.