AP Statistics Practice Quiz: Conditional Probability

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

Which of the following best describes the conditional probability P(A|B)?

A)The probability of event A occurring given that event B has occurred.B)The probability of event B occurring given that event A has occurred.C)The probability of both event A and event B occurring.D)The probability of event A occurring multiplied by the probability of event B occurring.

All Questions (9)

Which of the following best describes the conditional probability P(A|B)?

A) The probability of event A occurring given that event B has occurred.

B) The probability of event B occurring given that event A has occurred.

C) The probability of both event A and event B occurring.

D) The probability of event A occurring multiplied by the probability of event B occurring.

Correct Answer: A

The notation P(A|B) is read as 'the probability of A given B,' which represents the probability of event A happening under the condition that event B has already happened.

Given that the probability of events A and B both occurring is P(A and B) = 0.25, and the probability of event B occurring is P(B) = 0.50, what is the conditional probability P(A|B)?

A) 0.25

B) 0.50

C) 0.75

D) 1.25

Correct Answer: B

Using the formula for conditional probability, P(A|B) = P(A and B) / P(B). Substituting the given values, P(A|B) = 0.25 / 0.50 = 0.50.

The probability that a student takes Chemistry is 0.4. The probability that a student takes Chemistry and also takes Physics is 0.2. What is the probability that a student takes Physics given that they are taking Chemistry?

A) 0.2

B) 0.3

C) 0.4

D) 0.5

Correct Answer: D

Let C be the event of taking Chemistry and P be the event of taking Physics. We are given P(C) = 0.4 and P(C and P) = 0.2. We need to find P(P|C). Using the formula, P(P|C) = P(P and C) / P(C) = 0.2 / 0.4 = 0.5.

Which of the following correctly states the general multiplication rule for two events, A and B?

A) P(A and B) = P(A) * P(B)

B) P(A and B) = P(A) + P(B)

C) P(A and B) = P(A) * P(B|A)

D) P(A and B) = P(A|B) / P(B)

Correct Answer: C

The multiplication rule, derived from the conditional probability formula, states that the probability of two events both occurring is the probability of the first event multiplied by the conditional probability of the second event given the first has occurred: P(A and B) = P(A) * P(B|A).

The probability that a car needs an oil change is 0.7. If a car needs an oil change, the probability that it also needs a new air filter is 0.4. What is the probability that a car needs both an oil change and a new air filter?

A) 0.28

B) 0.40

C) 0.57

D) 1.10

Correct Answer: A

Let O be the event that a car needs an oil change and F be the event it needs a new air filter. We are given P(O) = 0.7 and P(F|O) = 0.4. We need to find P(O and F). Using the multiplication rule, P(O and F) = P(O) * P(F|O) = 0.7 * 0.4 = 0.28.

If P(A and B) = 0.3 and P(B) = 0.6, which expression correctly calculates P(A|B)?

A) 0.3 * 0.6

B) 0.6 / 0.3

C) 0.3 / 0.6

D) 0.3 + 0.6

Correct Answer: C

The formula for conditional probability is P(A|B) = P(A and B) / P(B). Plugging in the given values, the correct expression is 0.3 / 0.6.

For two events, A and B, it is known that P(A) = 0.5, P(B) = 0.8, and P(B|A) = 0.9. What is the value of P(A|B)?

A) 0.450

B) 0.563

C) 0.720

D) 0.900

Correct Answer: B

First, use the multiplication rule to find P(A and B): P(A and B) = P(A) * P(B|A) = 0.5 * 0.9 = 0.45. Then, use the conditional probability formula to find P(A|B): P(A|B) = P(A and B) / P(B) = 0.45 / 0.8 = 0.5625, which rounds to 0.563.

The formula P(A|B) = P(A and B) / P(B) can be algebraically rearranged to find the probability of the intersection of A and B. What is this rearranged formula?

A) P(A and B) = P(A|B) / P(B)

B) P(A and B) = P(B) / P(A|B)

C) P(A and B) = P(A|B) - P(B)

D) P(A and B) = P(A|B) * P(B)

Correct Answer: D

By multiplying both sides of the conditional probability formula by P(B), we isolate P(A and B). This gives the multiplication rule: P(A and B) = P(A|B) * P(B).

In a survey, 60% of respondents own a smartphone. Of those who own a smartphone, 25% also own a tablet. What percentage of respondents own both a smartphone and a tablet?

A) 15%

B) 25%

C) 42%

D) 85%

Correct Answer: A

Let S be the event of owning a smartphone and T be the event of owning a tablet. We are given P(S) = 0.60 and the conditional probability P(T|S) = 0.25. To find the probability of owning both, P(S and T), we use the multiplication rule: P(S and T) = P(S) * P(T|S) = 0.60 * 0.25 = 0.15, or 15%.