SAT Probability & Sampling Methods

Probability and sampling questions appear 2–4 times per SAT. You'll calculate basic probabilities, work with two-way frequency tables, and answer questions about survey design — whether a sample is representative, what conclusions can validly be drawn, and what would change the margin of error.

Study design interpretation questions are often harder than calculation questions and are underestimated by most test-takers. Understanding what makes a study valid and generalizable is just as important as arithmetic skills.

Basic probability: P(event) = favorable outcomes / total possible outcomes. For conditional probability from a two-way table, use only the relevant subgroup as the denominator — not the grand total.

P(A and B) = P(A) × P(B) only when A and B are independent events. Check independence before multiplying.

For sampling questions: random samples allow generalization to the population; larger samples reduce margin of error; voluntary response samples are biased toward strong opinions. Random assignment (used in experiments) allows causal conclusions; random sampling (used in surveys) does not.

Using the grand total instead of the subgroup total for conditional probability — the most common table calculation error on the SAT.

Assuming correlation implies causation in observational study questions. The SAT specifically tests this reasoning error; "associated with" is not the same as "caused by."

Confusing random assignment with random sampling. Random assignment allows causal claims; random sampling allows generalization to the population. These are different and not interchangeable.

The hardest probability questions on the SAT are usually the study design interpretation ones, not calculations. Practice reading study descriptions and asking: Is this a survey or experiment? Was sampling random? What can be validly concluded?

ScoreBooster's Data Analysis topic includes both probability calculations and study design questions with explanations of the logical reasoning behind each answer.