Bayes' Theorem in Artificial Intelligence (AI) is a fundamental principle used for probabilistic reasoning and decision-making under uncertainty. It describes how to update the probability of a hypothesis based on new evidence, using prior knowledge. Mathematically, it is expressed as P(H|E) = [P(E|H) * P(H)] / P(E), where P(H|E) is the probability of hypothesis H given evidence E, P(E|H) is the likelihood of observing E given H, P(H) is the prior probability of H, and P(E) is the overall probability of E. In AI, Bayes' Theorem is widely applied in areas like spam filtering, medical diagnosis, machine learning, and natural language processing to make data-driven predictions and improve decision-making.