Questions on Baye's Theorem
Bayes' Theorem Definition, Formula and 10 University-Level Solved Problems Definition of Bayes' Theorem Bayes' theorem is used to calculate the probability of an event after new information or evidence has become available. Let A and B be two events such that P(B) > 0. Then Bayes' theorem is P(A | B) = [P(B | A) P(A)] / P(B) Here: P(A | B) = posterior probability P(B | A) = likelihood P(A) = prior probability P(B) = probability of the evidence Prior Likelihood Posterior P(A) P(B | A) P(A | B) Figure 1: Bayes' theorem updates prior probability using new evidence. General Form If A 1 , A 2 , ..., A n form a partition of the sample space, then P(A i | B) = [P(A i ) P(B | A i )] / Σ P(A j ) P(B | A j ) Example 1: Two Machines A factory has two machines M 1 and M 2 . Machine M 1 produces 60% of the items and M 2 produces 40%. Their defective rates are 2% and 5%, respect...