algorithm-bayes-probability.md

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

$$ 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) \

$$

Bayes' Formula of probability

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