# Axioms of Probability

Let us define a **probability function**, $P$, with

**Domain**: all possible events.**Range**: $R$

$P$ satisfies the following:

- $P(S)=1;P(∅)=0$
- $A_{1}$, $A_{2}$, … are disjoint events then $P(∪_{i=1})=∑_{i=1}P(A_{i})$

Let us define a **probability function**, $P$, with

**Domain**: all possible events.**Range**: $R$

$P$ satisfies the following:

- $P(S)=1;P(∅)=0$
- $A_{1}$, $A_{2}$, … are disjoint events then $P(∪_{i=1})=∑_{i=1}P(A_{i})$