Bayes’ theorem is the mathematics of changing your mind without starting over.

Bayes' theorem is a rule of probability that describes how beliefs should change when new evidence arrives. It connects the probability of a hypothesis before seeing evidence with the probability after that evidence is observed. In effect, it provides a mathematical engine for learning from experience: start with what seems plausible, weigh how well the evidence fits each possibility, then update accordingly. Its compact formula powers decisions under uncertainty, from mundane predictions to sophisticated inference systems. Bayes' theorem turns fresh information into sharper estimates rather than starting from scratch. It is used primarily in statistics, artificial intelligence, and medical diagnosis.