AP®︎ Statistics: Topic 2.5 Flashcards

Master key terms and definitions for Topic 2.5 of AP Statistics – Mutually Exclusive Events to help you prep for quizzes and the AP exam.

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Term

Intersection

Definition

The event of all outcomes that belong to both A and B; written A ∩ B.

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Intersection
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The event of all outcomes that belong to both A and B; written A ∩ B.

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Joint Probability
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The probability of the intersection of A and B—the probability that both occur; P(A ∩ B), sometimes written P(AB)

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Mutually Exclusive or Disjoint Events
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Two events that cannot both occur in the same trial; they have no outcomes in common, so P(A ∩ B) = 0

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Criterion for Not Mutually Exclusive Events
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If P(A ∩ B) > 0, the events are not mutually exclusive

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Joint Probability in a Two-Way Table
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The probability of both categories occurring together; in a two-way table, cell count divided by total count

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Complement and Mutual Exclusivity
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An event and its complement are always mutually exclusive: P(A ∩ A^c) = 0

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Mutually Exclusive vs. Complements
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Complements are disjoint and together include all outcomes; mutually exclusive events only have to have no overlap

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Mutually Exclusive vs. Independent
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Mutually exclusive means the events cannot both occur in the same trial; independent means one event occurring does not change the probability of the other

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Structural vs. Numerical Justification
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Structural: use the event definitions and context to show no outcome can satisfy both events. Numerical: use the joint probability; in this topic, P(A ∩ B) = 0 supports mutually exclusive and P(A ∩ B) > 0 shows not mutually exclusive

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