AP®︎ Statistics: Topic 2.7 Flashcards

Master key terms and definitions for Topic 2.7 of AP Statistics – Independent Events and Unions of Events to help you prep for quizzes and the AP exam.

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Term

Independent Events

Definition

Events where knowing whether one occurs does not change the probability of the other; equivalently, when defined, P(A|B)=P(A) or P(B|A)=P(B), and P(A ∩ B)=P(A)P(B)

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Independent Events
Not Started

Events where knowing whether one occurs does not change the probability of the other; equivalently, when defined, P(A|B)=P(A) or P(B|A)=P(B), and P(A ∩ B)=P(A)P(B)

2.7.A2.7.A.1
Union of Events
Not Started

A ∪ B; the event that A or B or both occur

2.7.A2.7.A.2
General Addition Rule
Not Started

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

2.7.A2.7.A.3
Multiplication Rule for Independent Events
Not Started

If A and B are independent, then P(A ∩ B) = P(A)P(B)

2.7.A2.7.A.1
Mutually Exclusive Events
Not Started

Events that cannot occur together, so P(A ∩ B) = 0

2.7.A2.7.A.3
Neither A nor B
Not Started

The complement of the union: (A ∪ B)^c, so P(neither) = 1 − P(A ∪ B)

2.7.A2.7.A.2
Exactly One of A and B
Not Started

A or B but not both; P(exactly one) = P(A ∪ B) − P(A ∩ B) = P(A) + P(B) − 2P(A ∩ B)

2.7.A2.7.A.3
At Least One
Not Started

For events A and B, means A ∪ B; P(at least one) = P(A ∪ B) = 1 − P(A^c ∩ B^c); if A and B are independent, P(at least one) = 1 − [1 − P(A)][1 − P(B)]

2.7.A2.7.A.2
Independent Events Versus Mutually Exclusive Events
Not Started

Independent means P(A ∩ B)=P(A)P(B); mutually exclusive means P(A ∩ B)=0; if both events have positive probability, they cannot be both

2.7.A2.7.A.1
Intersection of Events
Not Started

A ∩ B; the event that both A and B occur

2.7.A2.7.A.3