# 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**

$$P\left(\Omega \right)=1$$

$$P\left(\overline{A}\right)=1-P\left(A\right)$$

$$P\left(A\cap B\right)=P\left(A|B\right)\xb7P\left(B\right)=P\left(B|A\right)\xb7P\left(A\right)$$

**In cas events A and B are independent**

$$P\left(A\cap B\right)=P\left(A\right)\xb7P\left(B\right)$$