Bayes’ Theorum

Theorum of total probability

A set of events (E1, E2, … En) be a partition of the Sample space S, and suppose that each of them has non-zero probability of occurrence, Let A be any even associated

\[\begin{split}p(A) = p(E_1) P(A | E_1) + P(E_2) . P(A | E_2) + … + P(E_n) P(A | E_n) \\ p(A) = \Sigma^n_{j = 1} P(E_j).P(A | E_j) \\\end{split}\]

Bayes’ Formula of probability

\[p(E_i | A ) = \frac{ P(E_i). P(A | E_i) }{ \Sigma^n_{j = 1} P(E_j).P(A | E_j) }\]