AP Biology / AP Statistics · Unit 2
Unit 2: Probability, Random Variables & Probability Distributions
Unit 2 is 15–25% of the AP Statistics exam and the mathematical foundation for every inference procedure in Units 3 and 4. In the 2026–27 redesign the geometric distribution and 'combining random variables' were removed — the exam now focuses tightly on probability rules, the binomial distribution, the normal distribution as a model, and sampling distributions.
Weight and scope
Exam weight: 15–25%. Expect ~6–10 MCQs and appearances on FRQ 2 (Practices 3 and 4).
Topic list (2026–27 CED)
- Introducing probability and simulation
- Estimating probabilities using simulation
- Random events, sample spaces, and probability
- Mutually exclusive events; the addition rule
- Conditional probability and independence; the multiplication rule
- Two-way tables and conditional probabilities
- Discrete random variables: mean and standard deviation
- Binomial distributions — mean, standard deviation, and probability
- Continuous random variables and probability density
- The normal distribution as a model for quantitative variables
- Sampling distribution of a sample proportion
- Sampling distribution of a sample mean; the Central Limit Theorem
- Sampling distribution of a difference in two sample proportions
- Sampling distribution of a difference in two sample means
What was removed
- Combining random variables (old Topic 4.9) — you no longer need to compute the mean or variance of a linear combination like X − Y.
- The geometric distribution (old Topic 4.12) — no more "first success on the kth trial" questions.
Formulas the exam expects you to use
| Situation | Formula |
|---|---|
| P(A or B), mutually exclusive | P(A) + P(B) |
| P(A or B), general | P(A) + P(B) − P(A ∩ B) |
| P(A and B), independent | P(A) · P(B) |
| P(A | B) | P(A ∩ B) / P(B) |
| Binomial P(X = k) | C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ |
| Binomial mean, SD | μ = np, σ = √(np(1−p)) |
| Sample proportion SD | √(p(1−p)/n) |
| Sample mean SD | σ / √n |
All of these are on the formula sheet. Your job is picking the right one, checking conditions, and executing.
Calculator moves
- binompdf(n, p, k) for exactly-k; binomcdf(n, p, k) for at-most-k.
- normalcdf(low, high, μ, σ) for area under a normal curve.
- invNorm(area, μ, σ) for the value with a given percentile.
- In Bluebook Desmos, use
normaldist(μ, σ).cdf(x)andbinomialdist(n, p).cdf(k).
Common mistakes
- Applying the Central Limit Theorem to a proportion (use np ≥ 10 and n(1−p) ≥ 10 instead).
- Treating "mutually exclusive" and "independent" as the same thing.
- Using binomcdf without stating the BINS conditions in an FRQ.
- Reporting μx̄ = μ but forgetting σx̄ = σ/√n on sampling distribution problems.
FAQ
Is the geometric distribution still on the AP Statistics exam?
No. In the 2026–27 redesign the College Board removed the geometric distribution (old Topic 4.12) and 'combining random variables' (old Topic 4.9) from the course. Only the binomial distribution and the normal distribution as a model remain.
What conditions do I need for a binomial distribution?
BINS: Binary outcomes, Independent trials, fixed Number of trials n, and constant probability of Success p. If the sample is drawn without replacement, the 10% condition (n ≤ 10% of the population) preserves approximate independence.
When does a sampling distribution become approximately normal?
For a sample proportion, np ≥ 10 and n(1−p) ≥ 10. For a sample mean, either the population is normal or n ≥ 30 (Central Limit Theorem). These conditions become the Normal/Large Counts checks for later inference procedures.
Keep going
Turn sampling distributions into inference points.
Cramapple's Unit 2 practice sets tie every sampling distribution problem to the Unit 3 or Unit 4 procedure it powers, so the transition to inference is seamless.
One-time purchase. No subscription.