Probability formulas

Complement Rule: 

Addition Rule:
For mutually exclusive: $$P\left(A\ ∪\ B\right)=P\left(A\right)+P\left(B\right)$$
For non-mutually exclusive: $$P\left(A\ ∪\ B\right)=P\left(A\right)+P\left(B\right)-P\left(A\ ∩\ B\right)$$

Multiplication Rule:
Independent events: $$P\left(A\ ∩\ B\right)=P\left(A\right)P\left(B\right)$$
Dependent events: $$P\left(A\ ∩\ B\right)=P\left(A\right)P\left(B/A\right)$$