AP Statistics Unit 2 Cheatsheet: Probability, Random Variables, and Probability Distributions

Start with the first 3 sections of the Unit 2 one-page cheatsheet below. The full sheet is a PDF you can print.

Two-Way Tables & Relative Frequencies

Joint relative frequency: cell count ÷ total count

Marginal relative frequency: row total ÷ grand total OR column total ÷ grand total

Conditional relative frequency: cell count ÷ row total (or column total, depending on condition)

Reading tables: Always identify what the denominator is. "Given" language signals conditional—restrict to that row or column first.

Graphical displays: Side-by-side bar charts, segmented bar charts, mosaic plots show association by comparing distributions across categories.

Mutually Exclusive & Conditional Probability

Mutually exclusive (disjoint): A and B cannot both occur → P(A ∩ B) = 0

Joint probability: P(A ∩ B) = probability both occur

Conditional probability: P(A | B) = P(A ∩ B) / P(B)

General multiplication rule: P(A ∩ B) = P(A) · P(B | A)

P(A | B) ≠ P(B | A) unless special conditions hold. Order matters.

Normal Distribution Basics

Characteristics: continuous, unimodal, bell-shaped, symmetric

Parameters: mean μ and standard deviation σ

Smaller σ → taller, more concentrated
Larger σ → shorter, more spread

Standard normal: μ = 0, σ = 1

Empirical rule (68–95–99.7):

≈68% within μ ± 1σ
≈95% within μ ± 2σ
≈99.7% within μ ± 3σ

The rest of the Unit 2 sheet

6 more sections are on the one-page PDF:

Probability Foundations
Discrete Random Variables & Distributions
Normal Probabilities & z-Scores
Independence & Union of Events
Binomial Distribution
Sampling Distributions & Central Limit Theorem

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Unit 2: Probability, Random Variables, and Probability Distributions on one page, aligned to the 2026-2027 course. Made and checked by the Fiveable Content Team.

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