Bayes' theorem
Also: Bayes' rule, Bayes rule, Bayes theorem
P(H | D) = P(D | H)·P(H) / P(D). It turns how well a hypothesis explains the data (likelihood) and how plausible it was beforehand (prior) into an updated belief (posterior).
P(H | D) = P(D | H) · P(H) / P(D)
Example
A disease affects 1% of people; a test is 99% sensitive with a 5% false-positive rate. After a positive result, P(disease) = 0.99·0.01 / (0.99·0.01 + 0.05·0.99) ≈ 0.167, only about 17%.