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AP Statistics Practice Quiz: Mutually Exclusive Events

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 9 questions to check your progress.

Question 1 of 9

According to the provided text, what is the primary definition of two mutually exclusive events?

All Questions (9)

According to the provided text, what is the primary definition of two mutually exclusive events?

A) They must occur at the same time.

B) They cannot occur at the same time.

C) The probability of one event is the opposite of the other.

D) Their joint probability is greater than 0.

Correct Answer: B

The content explicitly states that two events are mutually exclusive (disjoint) if they cannot occur at the same time.

If events A and B are mutually exclusive, what is the value of their joint probability, P(A and B)?

A) 1

B) 0.5

C) 0

D) It cannot be determined from the information given.

Correct Answer: C

The provided content specifies that for two mutually exclusive events, P(A and B) = 0.

A researcher finds that the joint probability of two events, C and D, is P(C and D) = 0. What can be concluded about these events?

A) Events C and D are not mutually exclusive.

B) Events C and D are certain to occur.

C) Events C and D are mutually exclusive.

D) Event C causes event D.

Correct Answer: C

The text states that if P(A and B) = 0, the two events are mutually exclusive.

The content uses the term 'disjoint' as a synonym for which of the following concepts?

A) Joint probability

B) Intersection of events

C) Mutually exclusive

D) Simultaneous events

Correct Answer: C

The text explicitly states, 'Two events are mutually exclusive (disjoint)...', indicating that the terms are synonymous.

What does the joint probability, P(A and B), represent according to the provided text?

A) The probability of either event A or event B occurring.

B) The probability of the intersection of events A and B.

C) The sum of the probabilities of event A and event B.

D) The probability that event A does not occur.

Correct Answer: B

The content defines the joint probability, P(A and B), as the probability of the intersection of events A and B.

Which statement provides the correct reasoning for why two events are mutually exclusive, based on the provided definitions?

A) The events are mutually exclusive because their joint probability is 1.

B) The events are mutually exclusive because they can and must occur at the same time.

C) The events are mutually exclusive because the probability of their intersection is zero.

D) The events are mutually exclusive because their individual probabilities are equal.

Correct Answer: C

The text connects the conceptual definition (cannot occur at the same time) with the mathematical one (P(A and B) = 0). The probability of their intersection being zero is the mathematical reason they are mutually exclusive.

Which of the following scenarios would prove that two events, X and Y, are NOT mutually exclusive?

A) The joint probability P(X and Y) is calculated to be 0.

B) It is observed that events X and Y occurred at the same time.

C) The probability of event X is 0.

D) The events are determined to be disjoint.

Correct Answer: B

Mutually exclusive events cannot occur at the same time. Therefore, an observation of them happening simultaneously is direct proof that they are not mutually exclusive.

Which of the following statements correctly synthesizes all the information provided about mutually exclusive events?

A) Two events are disjoint if they can occur at the same time, meaning their joint probability is greater than 0.

B) The joint probability, P(A and B), is the probability of the intersection of two events; if this probability is 0, the events are mutually exclusive, or disjoint.

C) Two events are mutually exclusive if the probability of their intersection is 1, meaning they are certain to occur together.

D) The concept of 'disjoint' means that the joint probability of two events is equal to the sum of their individual probabilities.

Correct Answer: B

This option correctly combines all three pieces of information: the definition of joint probability, the condition for it to be 0, and the terms 'mutually exclusive' and 'disjoint'.

If an analyst claims two events are 'disjoint', what must be true about the probability of their intersection?

A) The probability of their intersection must be greater than 0.

B) The probability of their intersection must be exactly 1.

C) The probability of their intersection is not relevant to them being disjoint.

D) The probability of their intersection must be 0.

Correct Answer: D

The text establishes that 'disjoint' is a synonym for 'mutually exclusive'. For mutually exclusive events, the probability of their intersection, which is the joint probability P(A and B), must be 0.