Addition and multiplication rules of probability, independence, and basic combinatorics used in intro statistics. Front: the term or rule. Back: definition or formula with a brief usage note.
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- Sample space
- The set of all possible outcomes in a probability experiment.
- Event (probability)
- A subset of the sample space; any collection of one or more outcomes from the experiment.
- Outcome
- A single result from a probability experiment; an element of the sample space.
- Probability (axiom)
- A number between 0 and 1 (inclusive) assigned to an event, where 0 means impossible and 1 means certain.
- Complement rule
- P(A^c) = 1 - P(A), where A^c is the complement of event A (all outcomes not in A).
- Mutually exclusive events
- Events that cannot occur together in the same experiment; their intersection is empty.
- Union of events
- The event 'A or B', containing all outcomes in A, B, or both; combines both sets without double-counting overlap.
- Addition rule (general form)
- P(A or B) = P(A) + P(B) - P(A and B); the subtraction corrects for double-counting the intersection.
- Addition rule (mutually exclusive events)
- When A and B are mutually exclusive: P(A or B) = P(A) + P(B), since P(A and B) = 0.
- Partition
- A collection of events that are mutually exclusive and exhaustive; their union is the entire sample space.
- Law of total probability
- P(A) = sum of P(A|B_i) * P(B_i) over all events B_i in a partition; breaks probability into conditional pieces.
- Conditional probability
- P(A|B) = P(A and B) / P(B); the probability of A given that B has occurred (B must have nonzero probability).
- Multiplication rule
- P(A and B) = P(A) * P(B|A); the joint probability equals the probability of one times the conditional probability of the other.
- Independent events
- Events where the occurrence of one does not affect the probability of the other; P(A|B) = P(A).
- Multiplication rule (independent events)
- When A and B are independent: P(A and B) = P(A) * P(B); no need for conditional probability.