identities about two-events probability

$\text{Pr}(A\cup B)=\text{Pr}(A)+\text{Pr}(B)-\text{Pr}(A\cap B)$
this is the addition rule

$\text{Pr}(A\cap B)=\text{Pr}(A)\cdot \text{Pr}(B|A)$
this is the multiplication rule

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

if A and B are mutually exclusive

• $\text{Pr}(A\cap B)=0$

if A and B are independent

• $\text{Pr}(A|B)=\text{Pr}(A)$
• $\text{Pr}(B|A)=\text{Pr}(B)$
• $\text{Pr}(A\cap B)=\text{Pr}(A)\cdot \text{Pr}(B)$