Physics, Chemistry, Mathematics Forums

While may be interesting to think about the future outcome of an event, many times it is important to know the likelihood of something once an event has happened.

Let B₁, B₂, …, B_n be n mutually exclusive and exhaustive events in a sample space S. Let A be any event in S intersecting every B_i, (i = 1,2,…,n) and \(P(A)\neq 0\). Then

\(P(B_i /A) = {\rm{ }}{{{\rm{P(B}}_{\rm{i}} )P(A/B_i )} \over {\sum\limits_{j = 1}^n {P(B_j )P(A/B_j )} }}\)

Think of it as A has happened and one of the Bs must have happened. So, here we are interested to know the probability that after A has happened what are the chances of a specific B happening.