### 3.1 Terminology

*A* and *B* are events

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

0 â‰¤ *P*(*A*) â‰¤ 1

*P*(*A*$|$*B*) = $\frac{P\text{(}A\xe2\u02c6\copyright B\text{)}}{P\text{(}B\text{)}}$

### 3.2 Independent and Mutually Exclusive Events

If $A$ and $B$ are independent, $P(A\xe2\u02c6\copyright B)=P\left(A\right)P\left(B\right),$ $P\left(A\right|B)=P(A)$ and $P\left(B\right|A)=P(B).$

If $A$ and $B$ are mutually exclusive, $P(A\xe2\u02c6\xaaB)=P\left(A\right)+P\left(B\right)$ and $P(A\phantom{\rule{0.2ems}{0ex}}\xe2\u02c6\copyright \phantom{\rule{0.2ems}{0ex}}B)=0.$

### 3.3 Two Basic Rules of Probability

**The multiplication rule:** *P*(*A* $\xe2\u02c6\copyright $ *B*) = *P*(*A*$|$*B*)*P*(*B*)

**The addition rule:** *P*(*A* $\xe2\u02c6\xaa$ *B*) = *P*(*A*) + *P*(*B*) - *P*(*A* $\xe2\u02c6\copyright $ *B*)