The concept of conditional probability discussed earlier takes into account information about the occurrence of one event to predict the probability of another event. This concept can be extended to revise probabilities based on new information and to determine the probability that a particular effect was due to specific cause. The procedure for revising these probabilities is known as Bayes theorem. The Principle was given by Thomas Bayes in 1763. By this principle, assuming certain prior probabilities, the posteriori probabilities are obtained. That is why Bayes’ probabilities are also called posteriori probabilities.
Bayes’ Theorem or Rule (Statement only):
Let A1, A2, A3, …….Ai, ……An be a set of n mutually exclusive and collectively
exhaustive events and P(A1), P(A2) …, P(An) are their corresponding probabilities. If B is
another event such that P(B) is not zero and the priori probabilities P(B|Ai) i =1,2…, n are