Probability Formulas

Product rule: probability $P(A \wedge B)$ of a conjunction of two events A and B: \[P(A \wedge B) = P(A\,|\,B) P(B) = P(B\,|\,A) P(A) \]
Sum rule: probability of a disjunction of two events A and B: \[P(A \vee B) = P(A) + P(B) - P(A \wedge B) \]
Theorem of total probability: if events $A_{1}, \ldots, A_{n}$ are mutually exclusive with $\sum_{i = 1}^{n} P(A_{i}) = 1$, then \[P(B) = \sum_{i = 1}^{n} P(B\,|\,A_{i}) P(A_{i})\]