Bayes' Theorem

Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event: \[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \] where \( P(A|B) \) is the probability of event A given that event B has occurred, \( P(B|A) \) is the probability of event B given that event A has occurred, \( P(A) \) is the probability of event A, and \( P(B) \) is the probability of event B.