Bayes' Theorem in AI (Artificial Intelligence)

Bayes' Theorem is a fundamental concept in probability theory and artificial intelligence. It describes the probability of an event based on prior knowledge of conditions related to the event. Mathematically, it is represented as:

[ P(A \mid B) = \frac{P(B \mid A) \times P(A)}{P(B)} ]

Where:

• ( P(A \mid B) ) is the probability of event ( A ) given event ( B ) has occurred.

• ( P(B \mid A) ) is the probability of event ( B ) given event ( A ) has occurred.

• ( P(A) ) and ( P(B) ) are the probabilities of events ( A ) and ( B ) respectively.

Bayes' Theorem is widely used in AI for tasks like probabilistic reasoning, spam filtering, medical diagnosis, and machine learning algorithms such as Naive Bayes classifiers.