Probability
Events, Operations with events, Complete system of events
Keywords:
Events
$$\Omega ,A$$

A is a subset of Ωsample space 
$$\varnothing $$

Impossible event 
$$\Omega $$

Sure event 
Operations with events
$$A\cup B=A+B$$

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

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

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

$$A\setminus B$$

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

$$\overline{A}$$

The event that occures, when A does not occure. 

$$B\subset A$$

B event entails A event.  
$$A\cap B=\varnothing $$

Events A end B are mutually exclusive events. 
Complete system of events
$$\sum _{i=1}^{n}{A}_{i}={A}_{1}+{A}_{2}+{A}_{3}+...+{A}_{n}=\Omega $$
$${A}_{i}\xb7{A}_{j}=\varnothing ,\forall \left(i\ne j\right)$$

Two events can not happen simultaneously. 