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AP Stats Unit 2 Practice Test

Unofficial practice for Unit 2 of AP Statistics: probability, random variables and probability distributions, as revised for 2026-27.

What is another name for a two-way table?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with the College Board. Bank checked October 14, 2026.

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All 50 questions

Topics 2.1 and 2.2: Two-way tables 9

  • A segmented bar chart has one bar for each of three grade levels, and each bar is split into walk, bus and car. The three bars are split in nearly the same way. What does this suggest? College Board, AP Statistics Course and Exam Description, topic 2.1, essential knowledge 2.1.A.3
  • A survey of 200 students finds that 48 of the 120 juniors and 52 of the 80 seniors have a part-time job. Among the seniors, what is the conditional relative frequency of having a job? College Board, AP Statistics Course and Exam Description, topic 2.2, essential knowledge 2.2.A.3
  • A survey of 200 students finds that 48 of the 120 juniors and 52 of the 80 seniors have a part-time job. Among the students with a job, what proportion are juniors? College Board, AP Statistics Course and Exam Description, topic 2.2, essential knowledge 2.2.A.3
  • A survey of 200 students finds that 48 of the 120 juniors and 52 of the 80 seniors have a part-time job. What is the joint relative frequency of being a junior with a job? College Board, AP Statistics Course and Exam Description, topic 2.2, essential knowledge 2.2.A.1
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Topics 2.1 and 2.2: Two-way tables, continued

  • A survey of 200 students finds that 48 of the 120 juniors and 52 of the 80 seniors have a part-time job. What is the marginal relative frequency of seniors? College Board, AP Statistics Course and Exam Description, topic 2.2, essential knowledge 2.2.A.2
  • The entries in the cells of a two-way table can be which two kinds of number? College Board, AP Statistics Course and Exam Description, topic 2.1, essential knowledge 2.1.A.1
  • In a survey, 40% of the juniors and 65% of the seniors have a part-time job. What does comparing these two conditional relative frequencies give? College Board, AP Statistics Course and Exam Description, topic 2.2, essential knowledge 2.2.B.1
  • What is another name for a two-way table? College Board, AP Statistics Course and Exam Description, topic 2.1, essential knowledge 2.1.A.1
  • Which graph displays the relationship between two categorical variables? College Board, AP Statistics Course and Exam Description, topic 2.1, essential knowledge 2.1.A.2

Topics 2.3 and 2.4: Simulation and basic probability 9

  • A fair coin lands heads on 7 of its first 10 tosses, and a student says tails is now due. Why is the student wrong? College Board, AP Statistics Course and Exam Description, topic 2.3, essential knowledge 2.3.A.7
  • A homework answer sheet lists four probabilities: 0, 0.004, 1 and 1.2. Which one must be a mistake? College Board, AP Statistics Course and Exam Description, topic 2.4, essential knowledge 2.4.A.3
  • A raffle drum holds 40 tickets: 12 from ninth graders, 18 from tenth graders and 10 from eleventh graders. One ticket is pulled at random. What is the probability that it came from a tenth grader? College Board, AP Statistics Course and Exam Description, topic 2.4, essential knowledge 2.4.A.2
  • A school bus is late on 12% of mornings. What is the probability that it is not late on a randomly chosen morning? College Board, AP Statistics Course and Exam Description, topic 2.4, essential knowledge 2.4.A.4
  • A simulation of a carnival spinner runs 400 trials, and the spinner lands on blue in 92 of them. What is the estimate of the probability of blue? College Board, AP Statistics Course and Exam Description, topic 2.3, essential knowledge 2.3.A.6
  • As the number of independent trials grows, what does the law of large numbers say about the long-run relative frequency of an event? College Board, AP Statistics Course and Exam Description, topic 2.3, essential knowledge 2.3.A.7
  • In the language of probability, what is an event? College Board, AP Statistics Course and Exam Description, topic 2.3, essential knowledge 2.3.A.3
  • Two fair four-sided dice, each numbered 1 to 4, are rolled. What is the probability that both show the same number? College Board, AP Statistics Course and Exam Description, topic 2.4, essential knowledge 2.4.A.2
  • What is the probability of the whole sample space of a random process? College Board, AP Statistics Course and Exam Description, topic 2.4, essential knowledge 2.4.A.1

Topics 2.5 to 2.7: Probability rules 14

  • A and B are mutually exclusive, with P(A) = 0.25 and P(B) = 0.35. What is P(A or B)? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.3
  • A basketball player makes each free throw with probability 0.8, independently of her other shots. What is the probability that she misses at least one of 3 free throws? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.1
  • A survey of 200 students finds that 48 of the 120 juniors and 52 of the 80 seniors have a part-time job. Are being a senior and having a job independent in this group? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.1
  • A vending machine jams on 5% of uses, and the change machine beside it is empty 20% of the time, independently of the jams. What is the probability that a visitor meets both problems? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.1
  • At a cafe, 30% of orders are for delivery, and 40% of delivery orders include a drink. What is the probability that a randomly chosen order is a delivery order with a drink? College Board, AP Statistics Course and Exam Description, topic 2.6, essential knowledge 2.6.A.2
  • At a library, 20% of returned books come back late. A late book has a damaged cover 30% of the time, and an on-time book 10% of the time. Given that a returned book has a damaged cover, what is the probability that it came back late, to two decimal places? College Board, AP Statistics Course and Exam Description, topic 2.6, essential knowledge 2.6.A.1
  • At a library, 20% of returned books come back late. A late book has a damaged cover 30% of the time, and an on-time book 10% of the time. What is the probability that a returned book has a damaged cover? College Board, AP Statistics Course and Exam Description, topic 2.6, essential knowledge 2.6.A.2
  • At a school, the probability that a student plays a sport is 0.5. Among students with a job, the probability of playing a sport is also 0.5. What does this show about the two events? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.1
  • Events A and B are mutually exclusive. What is P(A and B)? College Board, AP Statistics Course and Exam Description, topic 2.5, essential knowledge 2.5.A.2
  • One card is drawn from a standard deck. Which pair of events is mutually exclusive? College Board, AP Statistics Course and Exam Description, topic 2.5, essential knowledge 2.5.A.2
  • P(A and B) = 0.18 and P(B) = 0.60. What is P(A | B)? College Board, AP Statistics Course and Exam Description, topic 2.6, essential knowledge 2.6.A.1
  • P(A) = 0.4, P(B) = 0.3 and P(A and B) = 0.12. Are A and B mutually exclusive? College Board, AP Statistics Course and Exam Description, topic 2.5, essential knowledge 2.5.A.2
  • P(A) = 0.55, P(B) = 0.25 and P(A and B) = 0.15. What is P(A or B)? College Board, AP Statistics Course and Exam Description, topic 2.7, essential knowledge 2.7.A.3
  • Two cards are drawn from a standard 52-card deck without replacement. What is the probability that both are aces? College Board, AP Statistics Course and Exam Description, topic 2.6, essential knowledge 2.6.A.2

Topics 2.8 and 2.9: Random variables 6

  • A game costs $2 to play. A fair six-sided die is rolled, and the player wins $9 on a six and nothing otherwise. What is the expected net gain from one play? College Board, AP Statistics Course and Exam Description, topic 2.9, essential knowledge 2.9.A.2
  • A parcel takes 1, 2 or 4 days to arrive, with probabilities 0.50, 0.25 and 0.25, so the mean is 2 days. To two decimal places, what is the standard deviation of the delivery time? College Board, AP Statistics Course and Exam Description, topic 2.9, essential knowledge 2.9.A.3
  • A spinner has four equal sections numbered 1, 1, 2 and 3, and X is the number it lands on. What is P(X = 1)? College Board, AP Statistics Course and Exam Description, topic 2.8, essential knowledge 2.8.A.2
  • The number of text messages a student sends in a day is a discrete random variable. What makes it discrete? College Board, AP Statistics Course and Exam Description, topic 2.9, essential knowledge 2.9.A.2
  • Two fair six-sided dice are rolled, and X is the larger of the two numbers (or the shared number, if they match). What is P(X = 1)? College Board, AP Statistics Course and Exam Description, topic 2.8, essential knowledge 2.8.A.3
  • X is the number of goals a team scores in a match, with P(X = 0) = 0.30, P(X = 1) = 0.35, P(X = 2) = 0.20 and P(X = 3) = 0.15. What is the cumulative probability P(X ≤ 1)? College Board, AP Statistics Course and Exam Description, topic 2.8, essential knowledge 2.8.A.5

Topic 2.10: The binomial distribution 4

  • A basketball player keeps shooting until she makes a basket, and X is the number of shots she takes. Why is X not a binomial random variable? College Board, AP Statistics Course and Exam Description, topic 2.10, essential knowledge 2.10.A.1
  • A fair die is rolled 12 times, and X is the number of sixes. To three decimal places, what is P(X ≥ 1)? College Board, AP Statistics Course and Exam Description, topic 2.10, essential knowledge 2.10.E.1
  • An archer hits the bullseye on 40% of her shots, independently. In 3 shots, what is the probability of exactly 2 bullseyes? College Board, AP Statistics Course and Exam Description, topic 2.10, essential knowledge 2.10.E.1
  • At a plant nursery, 30% of cuttings take root, independently of one another. For 80 cuttings, what are the mean and standard deviation of the number that take root? College Board, AP Statistics Course and Exam Description, topic 2.10, essential knowledge 2.10.B.1

Topics 2.11 and 2.12: Normal and sampling distributions 8

  • A machine fills jars with amounts that are normally distributed with mean 500 grams and standard deviation 4 grams. By the empirical rule, about what percent of jars hold between 504 and 508 grams? College Board, AP Statistics Course and Exam Description, topic 2.11, essential knowledge 2.11.C.1
  • Ana scores 82 on a test with mean 70 and standard deviation 8. Ben scores 660 on a test with mean 500 and standard deviation 100. Both sets of scores are normal. Who did better relative to their own group? College Board, AP Statistics Course and Exam Description, topic 2.11, essential knowledge 2.11.F.1
  • By the central limit theorem, the sampling distribution of the mean of a random sample can be approximated by a normal distribution. What happens to the approximation as the sample gets larger? College Board, AP Statistics Course and Exam Description, topic 2.12, essential knowledge 2.12.A.4
  • Heights in a group are normally distributed with mean 64 inches and standard deviation 3 inches. By the empirical rule, the middle 95% of heights lie between which two values? College Board, AP Statistics Course and Exam Description, topic 2.11, essential knowledge 2.11.C.1
  • To mark off the most extreme 10% of a normal distribution on both sides, how much area goes in each tail? College Board, AP Statistics Course and Exam Description, topic 2.11, essential knowledge 2.11.E.2.iv
  • To simulate the sampling distribution of a statistic, random samples are generated from a population again and again. What is assumed about the population to do this? College Board, AP Statistics Course and Exam Description, topic 2.12, essential knowledge 2.12.A.2
  • Which description fits a normal curve? College Board, AP Statistics Course and Exam Description, topic 2.11, essential knowledge 2.11.A.3
  • Which phrase defines the sampling distribution of a sample statistic? College Board, AP Statistics Course and Exam Description, topic 2.12, essential knowledge 2.12.A.1

How this list was compiled: Our own questions, written to Unit 2 (Probability, Random Variables, and Probability Distributions, topics 2.1 to 2.12) of the College Board's AP Statistics Course and Exam Description, effective fall 2026, https://apcentral.collegeboard.org/media/pdf/ap-statistics-course-and-exam-description.pdf, read 2026-10-14. Each rule was read on 2026-10-14 in the essential knowledge statement named under its question, and every worked answer was recomputed from the numbers in its question. Licence: Own work.

How it works

This AP Stats Unit 2 practice test has 50 questions of our own on probability, random variables and probability distributions. It is unofficial and not affiliated with the College Board, which owns AP.

Read the full guide

What Unit 2 covers now

The College Board revised AP Statistics for the 2026-27 school year. In its course description, effective fall 2026 and read October 14, 2026, Unit 2 is Probability, Random Variables, and Probability Distributions, with twelve topics. The bank follows them: two-way tables (9 questions), simulation and basic probability (9), the probability rules (14), random variables (6), the binomial distribution (4), and normal and sampling distributions (8). Topics carry no weights in the description, so the spread is ours.

How the answers are checked

Each answer names the essential knowledge statement its rule was read in, and every worked answer was computed a second time from the numbers in its question.

  • Mutually exclusive: P(A and B) = 0. Independent: P(A and B) = P(A) × P(B). Two possible events are never both.
  • For a conditional probability from a two-way table, divide by the total of the given row or column, not by the table total.
  • With the empirical rule, sketch the curve and mark 1, 2 and 3 standard deviations before adding percentages.

Questions and answers

What is Unit 2 in AP Stats?

Probability, Random Variables, and Probability Distributions. The unit takes about 24 class periods and carries 15 to 25% of the multiple-choice section of the exam.

Isn't AP Stats Unit 2 Exploring Two-Variable Data?

It was, in the earlier nine-unit course. The course revised for 2026-27 has five units. Scatterplots, correlation and least-squares regression now sit in Unit 5, Regression Analysis, and two-way tables open the new Unit 2.

How many questions are on the AP Stats Unit 2 Progress Check?

About 42 multiple-choice questions and 2 free-response questions, by the course description. Teachers assign it in AP Classroom.

Do you need a calculator for AP Stats Unit 2?

Calculators are permitted on the AP Statistics Exam, by the College Board's exam page. Every question here can be worked by hand or with a basic calculator; the normal-curve questions need only the empirical rule and z-scores.

Are these the College Board's Unit 2 questions?

No. The 50 questions were written for this page from the topic list the College Board publishes for Unit 2. Its own questions stay in AP Classroom and on its exams.

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