Bayes' Theorem

Bayes' theorem, published posthumously by Reverend Thomas Bayes in 1763, provides a mathematical framework for updating beliefs in light of new evidence. The formula: P(H|E) = P(E|H) × P(H) / P(E). In words: the probability of a hypothesis (H) given evidence (E) equals the likelihood of seeing that evidence if the hypothesis is true, times the prior probability of the hypothesis, divided by the total probability of the evidence. This simple equation is the foundation of spam filters, medical diagnosis, machine learning, and criminal forensics. It formalizes what good reasoning does intuitively: you start with a belief, encounter evidence, and adjust your belief proportionally.