Bayes' Theorem

Posterior probability with a tree diagram

P(H|E) = P(E|H)·P(H) / [ P(E|H)·P(H) + P(E|¬H)·P(¬H) ]

Posterior P(H|E)

0.1538 (15.38%)

Evidence P(E)

0.0585 (5.85%)

Posterior given no evidence P(H|¬E)

0.0011

True-positive path P(H ∩ E)

0.009

False-positive path P(¬H ∩ E)

0.0495

About this calculator

The Bayes' Theorem Calculator finds the posterior probability P(H|E) from a prior, a sensitivity (true-positive rate), and a false-positive rate. It draws a probability tree showing how the prior splits into the true-positive path P(H ∩ E) and the false-positive path P(¬H ∩ E), reports the total evidence P(E), and updates the belief in the hypothesis. A clear way to see the base-rate fallacy in medical screening, spam filters, and diagnostic testing.