Multiplication Theorem

In Probability,

$P (\cap_{k=1}^{n} A_k) = P(A_1) P(A_2 | A_1) \cdots P(A_n | A_1 \cap A_2 \cdots A_{n-1})$

if independent

$P (\cap_{k=1}^{n} A_k) = \prod\limits_{k=1}^n (A_k)$

$P(A|B) = {P(A \cap B) \over P(B)} {=^{\text{ind}}} P(A)$