# 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¶

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