A and B are events

P(S) = 1 where S is the sample space

0 ≤ P(A) ≤ 1

P(A$|$B) = $\frac{P\text{(}A\cap B\text{)}}{P\text{(}B\text{)}}$

If $A$ and $B$ are independent, $P(A\cap B)=P\left(A\right)P\left(B\right),$ $P\left(A\right|B)=P(A)$ and $P\left(B\right|A)=P(B).$

If $A$ and $B$ are mutually exclusive, $P(A\cup B)=P\left(A\right)+P\left(B\right)$ and $P(A\cap B)=0.$

The multiplication rule: P(A $\cap$ B) = P(A$|$B)P(B)

The addition rule: P(A $\cup$ B) = P(A) + P(B) - P(A $\cap$ B)