Probability Formulas

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