Bayes' Theorem Calculator

A probability tree and a 1,000-person grid: see how prevalence drives the meaning of a positive test.

Prevalence P(V)5.0%Sensitivity P(+ | V)90%False-positive rate P(+ | Vᶜ)10.0%

Posterior P(V | +)

32.1%

Bayes' theorem

P(+)

14.0%

law of total probability

Positives that are false

67.9%

P(Vᶜ | −)

99.4%

negative predictive value

true positivefalse positivefalse negativetrue negative

Each dot is one person in a city of 1,000. The posterior P(V | +) is the share of blue among all dots that tested positive (blue + orange).