SAT / PSAT
SAT / PSAT Prep
History & Social Science
AP World History AP US History AP European History AP Human Geography AP US Government & Politics AP Psychology AP Macroeconomics AP Microeconomics
English
AP English Language & Composition AP English Literature & Composition
Math & Computer Science
AP Calculus AB/BC AP Precalculus AP Statistics AP Computer Science A AP Computer Science Principles
Sciences
AP Biology AP Chemistry AP Environmental Science AP Physics 1 AP Physics 2
World Languages & Arts
AP Spanish Language AP Art History AP Music Theory Start studying →
Unit 2 · 15–25% of Exam

Probability, Random Variables & Probability Distributions

The language of chance. Read two-way tables, apply the rules of probability, and reason about conditional probability and independence. Then meet random variables and the two workhorse models of the course — the binomial and the normal distribution — plus the sampling distributions that lead to inference.

12 topics
~24 class periods
15–25% of the exam
College Board aligned
← Back to AP Statistics

Choose your study tool

Six ways to master Unit 2 — pick whichever fits how you like to study.

Flashcards
24 interactive flashcards covering probability rules, conditional probability, random variables, and the binomial and normal distributions. Tap to flip.
Open flashcards →
Cheat Sheet
A one-page visual summary of Unit 2 — every probability rule, formula, and exam trap on a single screen.
Open cheat sheet →
Essentials
The core concepts plus a searchable glossary of every vocabulary term you need to know for the exam.
Open essentials →
Visual Review
A slide-by-slide walkthrough of Unit 2 with two-way tables, probability diagrams, and the binomial and normal curves.
Open visual review →
MCQ Practice
35 multiple-choice questions in College Board exam style — with full explanations of every answer.
Start practice →
FRQ Practice
A free-response question with model answers showing exactly how each part earns its point on the exam.
Start FRQ →

Topics in Unit 2

All 12 topics from the College Board CED, in order.

Topic 2.1
Representations for Two Categorical Variables
Two-way tables and segmented or side-by-side bar graphs for two categorical variables.
Topic 2.2
Summary Statistics for Two Categorical Variables
Marginal, joint, and conditional relative frequencies, and judging association.
Topic 2.3
Estimating Probabilities Using Simulation
Designing and running simulations to estimate the probability of an event.
Topic 2.4
Introduction to Probability
Probability as long-run relative frequency, the Law of Large Numbers, and sample spaces.
Topic 2.5
Mutually Exclusive Events
Disjoint events and the addition rule for events that cannot occur together.
Topic 2.6
Conditional Probability
P(A | B) — the probability of A given that B has occurred.
Topic 2.7
Independent Events & Unions of Events
Independence, the multiplication rule, and the general addition rule.
Topic 2.8
Introduction to Random Variables & Probability Distributions
Discrete random variables and the probability distributions that describe them.
Topic 2.9
Parameters of Random Variables
The mean (expected value) and standard deviation of a random variable, and combining variables.
Topic 2.10
The Binomial Distribution
The conditions for a binomial setting and its probabilities, mean, and standard deviation.
Topic 2.11
The Normal Distribution
The normal model, z-scores, the empirical rule, and finding probabilities and percentiles.
Topic 2.12
Sampling Distributions & the Central Limit Theorem
The distribution of a sample statistic and why it becomes approximately normal.

About Unit 2

Unit 2 gives you the tools to reason about chance. It opens with two categorical variables — two-way tables and the marginal, joint, and conditional relative frequencies you read from them — then builds the rules of probability: the Law of Large Numbers, the addition rule for mutually exclusive events, conditional probability, and the multiplication rule for independent events. Simulation is used throughout to estimate probabilities when exact calculation is hard.

The unit then introduces random variables — rules that assign numbers to the outcomes of a chance process — and their probability distributions, each with a mean (expected value) and a standard deviation. You'll study the two most important models in the course: the binomial distribution (a fixed number of independent success/failure trials) and the normal distribution (the bell curve, with z-scores and the empirical rule). It closes with sampling distributions and the Central Limit Theorem, the bridge from probability to the inference of Units 3–5.

This unit is 15–25% of the AP Statistics exam and takes about 24 class periods. The four statistical practices below run through every topic:

Practice 1
Formulate Questions — pose a valid investigative question
Practice 2
Collect Data — justify methods and identify probability models
Practice 3
Analyze Data — calculate probabilities and distribution parameters
Practice 4
Interpret Results — interpret probabilities and conclusions in context
Up next
Unit 3: Inference for Categorical Data: Proportions
Start Unit 3 →