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
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The set of all possible outcomes in a probability experiment.- Event (probability)
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A subset of the sample space; any collection of one or more outcomes from the experiment.- Outcome
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A single result from a probability experiment; an element of the sample space.- Probability (axiom)
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A number between 0 and 1 (inclusive) assigned to an event, where 0 means impossible and 1 means certain.- Complement rule
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P(A^c) = 1 - P(A), where A^c is the complement of event A (all outcomes not in A).- Union of events
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The event 'A or B', containing all outcomes in A, B, or both; combines both sets without double-counting overlap.- Addition rule (general form)
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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)
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When A and B are mutually exclusive: P(A or B) = P(A) + P(B), since P(A and B) = 0.- Partition
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A collection of events that are mutually exclusive and exhaustive; their union is the entire sample space.- Law of total probability
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P(A) = sum of P(A|B_i) * P(B_i) over all events B_i in a partition; breaks probability into conditional pieces.- Multiplication rule
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P(A and B) = P(A) * P(B|A); the joint probability equals the probability of one times the conditional probability of the other.- Multiplication rule (independent events)
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When A and B are independent: P(A and B) = P(A) * P(B); no need for conditional probability.- Dependent events
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Events where the occurrence or non-occurrence of one affects the probability of the other.- Tree diagram
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A visual representation of all possible outcomes and their probabilities, showing branches for each event and path.- Venn diagram
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A visual representation using overlapping circles or shapes to show relationships between events and their intersections.
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