AP Statistics Probability Quiz – Free PDF

Contents

This ap statistics probability quiz asks 10 multiple-choice questions on probability and random variables, and each answer comes with a short explanation.

This quiz has 10 multiple-choice questions on two-way tables, probability rules, independence, simulation, and the mean and standard deviation of a random variable. Choose the single best answer, and read each explanation to see why the other choices fail.

AP StatisticsCommon Core: AP Statistics Unit 2 (2026-27)

🎯 Probability and Random Variables – AP Statistics math quiz

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Question 1

A club of 100 students is classified by class and favorite food. What is the probability that a randomly chosen senior prefers pizza?

Students by class and favorite food.

A 0.18

B 0.375

C 0.48

D 0.36

Question 2

The probability that it rains tomorrow is 0.35. What is the probability that it does not rain?

A 0.35

B 1.35

C 0.65

D 0.45

Question 3

Of 120 students, 33 take only Spanish, 15 take both, 21 are in band only, and 51 do neither. What is the probability a student takes Spanish or is in band?

Counts in each region.

A 0.700

B 0.575

C 0.125

D 0.450

Question 4

A die is rolled once. Event A is rolling an even number and event B is rolling a number greater than 4. Are A and B mutually exclusive?

A Yes, because P(A) + P(B) is less than 1

B Yes, because the die is rolled only once

C No, because P(A) is not equal to P(B)

D No, because rolling a 6 is in both events

Question 5

For events A and B, P(A) = 0.4, P(B) = 0.5 and P(A and B) = 0.2. Which statement is correct?

A Not independent, since the events can occur together

B Independent, since 0.4 × 0.5 = 0.2

C Not independent, since 0.4 + 0.5 = 0.9, not 0.2

D Independent, since the events are mutually exclusive

Question 6

A basketball player makes 40% of her shots. Which assignment of random digits can simulate one shot?

A Digits 0 to 3 are a make and 4 to 9 are a miss

B Digits 0 to 4 are a make and 5 to 9 are a miss

C Digit 4 is a make and all other digits are a miss

D Digits 0 to 3 are a make, 4 to 7 are a miss, ignore 8 and 9

Question 7

The probability histogram shows the number of goals X scored by a team in a game. What is the mean of X?

Probability distribution of X.

A 1.9

B 1.5

C 2.0

D 0.25

Question 8

In a claw game the mean number of prizes per play is 1.75. Which interpretation is correct?

A On every play a player wins exactly 1.75 prizes

B The most likely result of a play is 1.75 prizes

C After 4 plays a player wins exactly 7 prizes

D Over many plays, the average number of prizes per play is close to 1.75

Question 9

Two games both have a mean payout of $15. Game A pays $10 or $20 with equal probability. Game B pays $14 or $16 with equal probability. Which statement is true?

A Game A has the larger standard deviation

B The standard deviations are equal because the means are equal

C Game B has the larger standard deviation

D The standard deviations cannot be compared

Question 10

The probability of rain is 0.3. The bus is late with probability 0.2 if it rains and 0.05 if it does not. What is the probability that the bus is late?

Tree for the bus.

A 0.060

B 0.250

C 0.095

D 0.035

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Joint, marginal and conditional relative frequencies come from dividing by the grand total, a row or column total, or the given group.
Complement rule: P(not A) = 1 – P(A). Addition rule: P(A or B) = P(A) + P(B) – P(A and B).
Conditional probability: P(B|A) = P(A and B)/P(A). Events are independent when P(B|A) = P(B).
A simulation estimates a probability by repeating a random process many times with a clear digit assignment.
A discrete random variable has mean sum of x times P(x), and standard deviation the square root of the weighted squared deviations.