AP Stat - Probability Rules!

Front

What is the definition of conditional probability?

Back

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of A given B.

Front

What is the formula for calculating conditional probability?

Back

P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both A and B occurring.

Front

What does it mean for two events to be mutually exclusive?

Back

Two events are mutually exclusive if they cannot occur at the same time. For example, rolling a die cannot result in both a 2 and a 5.

Front

What is the formula for the probability of the union of two mutually exclusive events?

Back

P(A ∪ B) = P(A) + P(B) for mutually exclusive events.

Front

What is the definition of independent events?

Back

Two events are independent if the occurrence of one event does not affect the probability of the other event occurring.

Front

What is the formula for the probability of the union of two independent events?

Back

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) for independent events.

Front

How do you calculate the probability of at least one event occurring in a series of trials?

Back

P(at least one) = 1 - P(none). For example, if the probability of an event is p, then P(none) = (1 - p)^n.

Front

What is the complement rule in probability?

Back

The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring: P(not A) = 1 - P(A).

Front

What is the definition of joint probability?

Back

Joint probability is the probability of two events occurring at the same time, denoted as P(A ∩ B).

Front

What is the definition of a sample space in probability?

Back

A sample space is the set of all possible outcomes of a probability experiment.