AP Statistics Unit 4: Probability, Random Variables, and Probability Distributions

Unit 4 covers probability and random variables: probability rules, conditional probability, and the binomial and geometric distributions. Choosing the right distribution is most of the work.

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100 questions11 CED topics100% with a figure
How this unit behaves

What 100 questions on it look like

It spans 11 CED topics, which is wide enough that "I've studied this unit" is not a meaningful statement. Track your accuracy by topic, not by unit.

100% of the questions come with a figure — a graph, diagram or data display. Reading the figure correctly is most of the work before any content knowledge applies.

The Geometric Distribution64
Mutually Exclusive Events11
Mean and Standard Deviation of Random Variables5
Independent Events and Unions of Events5
Introduction to the Binomial Distribution4
Combining Random Variables3
Introduction to Probability2
Estimating Probabilities Using Simulation2

Questions per CED topic, top 8 of 11.

From the bank

Three real probability, random variables, and probability distributions questions

Drawn from the practice pool, not from the mock papers.

Mutually Exclusive Events · Using Probability and Simulation · with figure

In farm stand cooperative fjord cycle, P(uses the receipt code) = 0.30, P(reports cashless payment use) = 0.20, and P(both) = 0.08. Which expression gives the probability of at least one of the two events?

  1. A0.30 + 0.20 - 0.08correct
  2. B0.08
  3. C0.30 × 0.20
  4. DP(A) + P(B), which double-counts students or outcomes that fall in both events
  5. E0.30 + 0.20
Why A is correct

For a union, add the two probabilities and subtract the overlap: 0.30 + 0.20 - 0.08 = 0.42.

Union probability for farm stand cooperative fjord cycle: the important cue is the farm stand cooperative fjord cycle setting. Match the method to the way the data are collected or the statistic is computed, then state the conclusion in the language of the stem.

Common mistakes. Union probability for farm stand cooperative fjord cycle: Do not double-count people or outcomes in both events.

Mean and Standard Deviation of Random Variables · Using Probability and Simulation · with figure

A fundraiser game costs $3 to play. A player wins $20 with probability 0.10, wins $5 with probability 0.20, and wins $0 otherwise. What is the player's expected net gain per play?

  1. A$2.00
  2. B-$3.00
  3. C$0.00correct
  4. D$3.00
  5. E$5.00
Why C is correct

The expected payout is 20(0.10) + 5(0.20) + 0(0.70) = 3 dollars. After subtracting the $3 cost, the expected net gain is $0.

Expected value of a random variable: in the "A fundraiser game costs $3 to play. A player wins $20 with probability 0.10, wins $5 with probability 0.20, and wins $0 otherwise. What is the player's expected net gain per play?" setting, especially Mean and Standard Deviation of Random Variables, compute the statistic and then describe what it means for the scenario. The professional check is to keep the values 3, 20, 0.10, 5, 0.20, the expected value method, and the final answer choice aligned with Probability, Random Variables, and Probability Distributions.

Common mistakes. For the stem cue "A fundraiser game costs $three to play. A player wins $twenty with probability zero point one zero, wins $five with probability zero point two zero, and wins $zero otherwise. What", a likely mistake is this subtracts the cost but ignores the expected payout. Keep the calculation or conclusion tied to the original context.

The Geometric Distribution · Using Probability and Simulation · with figure

Each independent trial has success probability 0.25. What is the probability that the first customer survey response occurs on trial 4?

  1. A0.8945
  2. B0.3164
  3. C0.0039
  4. D0.1055correct
  5. E0.25
Why D is correct

First success on trial 4 means 3 failures followed by success: (0.75)^3(0.25) = 0.1055.

geometric probability for first customer survey response: in the "Each independent trial has success probability 0.25. What is the probability that the first customer survey response occurs on trial 4?" setting, especially first customer survey response; survey response, match the probability rule to the event wording before calculating. The professional check is to keep the values 0.25, 4, the geometric probability method, and the final answer choice aligned with Probability, Random Variables, and Probability Distributions.

Common mistakes. For the stem cue "Each independent trial has success probability zero point two five. What is the probability that the first customer survey response occurs on trial four?", a likely mistake is this is the probability of success on one trial, not first success on trial k. Keep the calculation or conclusion tied to the original context.

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FAQ

Probability, Random Variables, and Probability Distributions questions

Binomial or geometric?

Binomial counts successes in a fixed number of trials. Geometric counts trials until the first success.

How do I recognise conditional probability?

The phrase "given that" restricts the sample space — the denominator becomes only that group.
Last reviewed 2026-08-28. Unit and topic names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.
Topic by topic

Worked questions by topic

1 of this unit’s topics have enough practice questions for a page of their own.

The Geometric Distribution64 questions
Same course
Unit 1: Exploring One-Variable Data460 questionsUnit 2: Exploring Two-Variable Data295 questionsUnit 3: Collecting Data190 questionsUnit 5: Sampling Distributions70 questionsUnit 6: Inference for Categorical Data: Proportions107 questionsUnit 7: Inference for Quantitative Data: Means63 questionsUnit 9: Inference for Quantitative Data: Slopes133 questions

Practise probability, random variables, and probability distributions until the reasoning is automatic.

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