Probability

# Probability of an event

## Keywords:

$P\left(A\right)=\frac{\left|A\right|}{\left|\Omega \right|}$

|A| - number of ways an event can happen

|Ω| - total number of outcomes

$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$
 $P\left(\varnothing \right)=0$ Probability of an impossible event $P\left(\Omega \right)=1$ Probability of a sure event
$P\left(\overline{A}\right)=1-P\left(A\right)$
$P\left(A\cap B\right)=P\left(A|B\right)·P\left(B\right)=P\left(B|A\right)·P\left(A\right)$
 $P\left(A\cap B\right)=P\left(A\right)·P\left(B\right)$ In cas events A and B are independent