AP Statistics Flashcards: Independent Events and Unions of Events
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: June 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What is the formula for P(A and B) if events A and B are independent?
If events A and B are independent, the probability of both occurring is calculated by multiplying their individual probabilities: P(A and B) = P(A) * P(B).
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What is the formula for P(A and B) if events A and B are independent?
If events A and B are independent, the probability of both occurring is calculated by multiplying their individual probabilities: P(A and B) = P(A) * P(B).
A student is chosen from a school. P(in Band) = 0.2, P(in Sports) = 0.5, and P(in Band or Sports) = 0.6. What is P(in Band and Sports)?
Rearranging the addition rule, P(A and B) = P(A) + P(B) - P(A or B). So, P(Band and Sports) = 0.2 + 0.5 - 0.6 = 0.1.
What does the probability of the union of two events, P(A or B), represent?
The probability of the union of A and B, P(A or B), is the probability that event A, event B, or both events occur.
If events A and B are independent, what is the relationship between the conditional probability P(A|B) and P(A)?
If events A and B are independent, the conditional probability P(A|B) is equal to the probability of A, meaning P(A|B) = P(A).
The probability of a sunny day is 0.7 and the probability of a windy day is 0.4. If these events are independent, what is the probability it is both sunny and windy?
Since the events are independent, P(Sunny and Windy) = P(Sunny) * P(Windy) = 0.7 * 0.4 = 0.28.
State the general addition rule for calculating P(A or B).
The general addition rule states that the probability of A or B occurring is P(A or B) = P(A) + P(B) - P(A and B).
Given P(A) = 0.6, P(B) = 0.3, and P(A and B) = 0.1, calculate P(A or B).
Using the addition rule, P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.3 - 0.1 = 0.8.
Define "independent events".
Two events, A and B, are independent if knowing that event A occurs does not change the probability of event B occurring.
What are the three mathematical conditions that are true if events A and B are independent?
If A and B are independent, then P(A|B) = P(A), P(B|A) = P(B), and P(A and B) = P(A) * P(B).
Why is the term P(A and B) subtracted in the general addition rule?
The term P(A and B) is subtracted because the outcomes where both A and B occur are counted in both P(A) and P(B), so it must be removed once to avoid double-counting.
If P(B|A) = 0.2 and P(B) = 0.5, are events A and B independent?
No, events A and B are not independent because for independence, P(B|A) must equal P(B), but 0.2 is not equal to 0.5.