Find probabilities, including conditional probabilities from two-way tables. It is part of Problem-Solving and Data Analysis in the Math section. The book teaches it in Chapter 25, Probability, Sampling, Inference and Evaluating Claims, with 6 practice questions, and tests it 2 more times across the two full-length practice tests.
About Chapter 25
This chapter covers the last three Problem-Solving and Data Analysis skills: Probability and conditional probability; Inference from sample statistics and margin of error; and Evaluating statistical claims: observational studies and experiments. They need less arithmetic than most Math questions and more careful reading.
Two questions settle most of these items. For probability, ask: which group am I choosing from? That group's total is the denominator. For studies and surveys, ask: how were the subjects chosen, and how were they assigned to groups? The answers tell you which conclusions the data can support.
What the questions look like
A probability from counts, such as "If one of these students is selected at random, what is the probability that…"
A conditional probability from a two-way table, a table that sorts the same people or things by two categories at once, with row and column totals.
An estimate for a whole population from a random sample, such as the number of students at a school who would answer yes.
An interpretation of a margin of error, the amount added to and subtracted from a sample estimate to give a range of plausible values for the population.
A question about how sample size affects the margin of error.
A choice of the conclusion a study supports: cause or only association, and for which group of people.
How to recognize them
A population is the whole group a question is about, such as all students in a district. A sample is the part of the population that was actually measured. A random sample gives every member of the population a chance to be chosen, so it tends to represent the population fairly.
"selected at random" with counts or a table: Probability = favorable outcomes ÷ total outcomes
"given that," "if one of the … is selected," "of those who …": Conditional probability. The denominator is the restricted group.
"random sample," "based on the sample," "best estimate": Apply the sample proportion or mean to the population
"margin of error," "plausible," "most appropriate conclusion": Estimate ± margin gives plausible population values
"randomly assigned," "treatment," "control group": Experiment. Cause can be concluded.
"surveyed," "observed," "recorded," "compared people who …": Observational study. Association only.
Common traps
Using the grand total for a conditional probability: The question restricts the group with "given that" or "of the."
Reversing the condition: Check which group follows "given that"; that group is the denominator.
Treating categories as equally likely: The categories have different counts, so 1/3 or 1/2 is rarely right.
Reading the sample value as the population value: The answer says "exactly" or ignores the margin of error.
Applying the margin of error to individuals: The range describes a mean or proportion, not single people or days.
Generalizing beyond the population sampled: The conclusion names a larger group, such as "all teenagers in the country."
Claiming cause without random assignment: The study only surveyed or observed.
Thinking volunteers rule out cause: Random assignment still supports cause for subjects like the volunteers.
Video lessons
Two short lessons from independent YouTube creators, chosen for this skill. The notes are ours; the videos belong to their creators, who are not affiliated with this site.
Probability, including conditional probability (Settele Tutoring — SAT® Lessons and Strategies, 6:27). Watch for: Using the right row or column total as the denominator.
Conditional probability with two-way tables (Bao Le Math, 7:03). Watch for: Reading “given that” as a restriction to one row or column.
Practice this skill
The full method, worked examples and 6 practice questions with every answer choice explained are in Chapter 25 of the book and in the study workspace, where an AI coach can talk you through each one.
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