# Probability of an event

Keywords: probability of an event, impossible event, sure event, independent event
$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}$

|A| - number of ways an event can happen

|Ω| - total number of outcomes

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$

Probability of an impossible event

$P\left(\varnothing \right)=0$

Probability of a sure event

$P\left(\Omega \right)=1$
$P\left(\overline{A}\right)=1-P\left(A\right)$
$P\left(A\cap B\right)=P\left(A|B\right)·P\left(B\right)=P\left(B|A\right)·P\left(A\right)$

In cas events A and B are independent

$P\left(A\cap B\right)=P\left(A\right)·P\left(B\right)$