## Multiplication Rule in Probability

If $A$ and $B$ are two events in a probability experiment such that $P(A)\neq 0$ and $P(B)\neq 0$, then the probability that both the events occurs simultaneously is

\begin{aligned} P(A\cap B)& = P(A|B)\times P(B)\\ &=P(B|A)\times P(A) \end{aligned}

In case of independent events, the probability that both the events occurs simultaneously is

\begin{aligned} P(A\cap B)& = P(A)\times P(B) \end{aligned}