AP Statistics Flashcards: Conditional Probability
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
In the context of conditional probability, what does the notation P(A|B) represent?
It represents the probability of event A occurring under the condition that event B has already occurred.
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In the context of conditional probability, what does the notation P(A|B) represent?
It represents the probability of event A occurring under the condition that event B has already occurred.
Why must P(B) be greater than zero in the formula for P(A|B)?
It is required because division by zero is undefined, and you cannot condition on an event that has zero probability of occurring.
How can the General Multiplication Rule be derived from the conditional probability formula?
It is derived by algebraically rearranging the conditional probability formula, P(B|A) = P(A and B) / P(A), to solve for P(A and B).
If P(Rain and Clouds) = 0.3 and P(Clouds) = 0.6, what is the probability of rain given that it is cloudy?
P(Rain|Clouds) = P(Rain and Clouds) / P(Clouds) = 0.3 / 0.6 = 0.5.
What is the General Multiplication Rule for the probability of two events occurring?
The rule states that the probability of events A and B both occurring is P(A and B) = P(A) * P(B|A).
What is the formula for the conditional probability of event A given event B, denoted P(A|B)?
The formula is P(A|B) = P(A and B) / P(B), where P(B) > 0.
How does the conditional probability formula relate to the idea of a 'reduced sample space'?
The denominator, P(B), represents the new, reduced sample space because we are only considering outcomes where event B has occurred.
Define conditional probability in words.
Conditional probability is the likelihood of an event occurring, given that another event has already happened.
A student is chosen at random. P(in band) = 0.25 and P(in band and on honor roll) = 0.15. Find the probability the student is on the honor roll given they are in the band.
P(Honor Roll | Band) = P(Honor Roll and Band) / P(Band) = 0.15 / 0.25 = 0.6.
The probability of a flight being on time is 0.8. Given the flight is on time, the probability of luggage arriving is 0.9. What is the probability of a flight being on time AND the luggage arriving?
Using the multiplication rule, P(On Time and Luggage) = P(On Time) * P(Luggage|On Time) = 0.8 * 0.9 = 0.72.