# Events, Operations with events, Complete system of events

## Events

**A is a subset of Ω-sample space**

$$\Omega ,A$$

**Impossible event**

$$\varnothing $$

**Sure event**

$$\Omega $$

## Operations with events

The event that occures, when either A or B or both occur.

$$A\cup B=A+B$$

The event that occures, when both A and B occur simultaneously.

$$A\cap B=A\xb7B$$

The event that occures, when A accumres, but B not.

$$A\setminus B$$

The event that occures, when A does not occure.

$$\overline{A}$$

B event entails A event.

$$B\subset A$$

Events A end B are mutually exclusive events.

## Complete system of events

$$\sum _{i=1}^{n}{A}_{i}={A}_{1}+{A}_{2}+{A}_{3}+...+{A}_{n}=\Omega $$

**Two events can not happen simultaneously.**

$${A}_{i}\xb7{A}_{j}=\varnothing ,\forall \left(i\ne j\right)$$

Keywords: Events, Operations with events, Complete system of events