# Bayes' Theorem

*Math & Statistics — Finicade finance glossary*

Bayes' theorem tells you how to update a probability when new evidence arrives, combining prior belief with the likelihood of what you observed. Its most useful lesson is about base rates: a 99% accurate test for a condition affecting 1 in 10,000 people still produces mostly false positives, because the rare truth is swamped by the common error. Ignoring that is the base rate fallacy.

**Formula:** `P(A|B) = P(B|A) × P(A) ÷ P(B)`

**Also known as:** Bayes rule, Bayes theorem, Bayes law

**Related terms:** [Conditional Probability](https://finicade.com/glossary/conditional-probability), [Bayesian Inference](https://finicade.com/glossary/bayesian-inference), [Probability](https://finicade.com/glossary/probability), [Hypothesis Test](https://finicade.com/glossary/hypothesis-test), [Base Rate Fallacy](https://finicade.com/glossary/base-rate-fallacy)

Source: https://finicade.com/glossary/bayes-theorem