Bayes' Theorem

Bayes’ Theorem:

 Bayes’ Theorem is a way of finding a Probability when we know certain other probabilities.

The formula is: P(A|B) = P(A) P(B|A) / P(B)

Where

P(B|A)=How often B happens given that A happens

P(A|B)= How often A happens given that B happens

P(A) = How likely A is on its own

P(B) = How likely B is on its own

Description:

Let {E1,E2,…,En} be a set of events associated with a sample space S, where all the events E1,E2,…,En have nonzero probability of occurrence and they form a partition of S. Let A be any event associated with S, then according to Bayes theorem,

Explanation:

According to conditional probability formula,

Using multiplication rule of probability,                   

 

Using total probability theorem,

 

 

From equations 2 and 3: