Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). The probability of an event E is P(E) = number of favorable outcomes / total number of possible outcomes.
The addition rule states P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events (that cannot both happen), this simplifies to P(A or B) = P(A) + P(B).
The multiplication rule states P(A and B) = P(A) × P(B|A), where P(B|A) is the conditional probability of B given A occurred. For independent events, P(A and B) = P(A) × P(B).
Compound events combine simple events using AND (intersection) or OR (union). Tree diagrams help visualize sequential probability calculations by showing all possible outcomes at each stage of a multi-step experiment.