SAT Math · Problem-Solving & Data Analysis

Probability on the Digital SATWhat it tests, how to approach it, and where students get trapped

One-event and conditional probability, usually read out of two-way frequency tables — the key is identifying the correct restricted group.

Try the Sample QuestionsOpen the Question Bank

Probability in Our Question Bank

34

Total questions

12

Easy

18

Medium

4

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Problem-Solving & Data Analysis.

What the SAT Actually Tests

SAT probability questions often use a two-way frequency table that splits a sample by two characteristics. You may compute the probability of one characteristic, an overlap between characteristics, or one characteristic given the other (conditional probability).

The whole skill reduces to choosing the right denominator. "What fraction of left-handed students are seniors" restricts the world to left-handed students — that row or column total is your denominator, not the grand total. Underline the 'given' group in the question, find its total in the table, then count the overlap.

Common Probability Question Patterns

Pattern 1Compute a basic probability from equally likely outcomes or category counts.
Pattern 2Read an overlap from a two-way table or described sample space.
Pattern 3Compute a conditional probability using only the stated subgroup as the denominator.

A Step-by-Step Strategy

  1. 1

    Define the event

    State exactly what outcome counts as favorable and whether a condition restricts the group.

  2. 2

    Choose the denominator

    Use the whole sample for an unconditional event and the given subgroup for a conditional event.

  3. 3

    Count the overlap

    Locate outcomes satisfying every required characteristic.

  4. 4

    Simplify and sanity-check

    Reduce the fraction when useful and confirm the result lies between 0 and 1.

Original Probability Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy
Each face of a fair 8-sided die is labeled with a number from 1 through 8, with a different number appearing on each face. If the die is rolled one time, what is the probability of rolling a 5?
Question 2easy
A box contains 24 crayons: 6 red, 4 blue, 8 yellow, and 6 green. If one crayon is selected at random, what is the probability it is yellow?
Question 3hard
A nursery has 8 rows of roses and 5 rows of lavender. Each row of roses has 3 plants that are at least 3 feet tall, and each row of lavender has the same number of plants that are at least 3 feet tall. If a plant is selected at random from the plants that are at least 3 feet tall, the probability that it is lavender is 58. The nursery then adds 4 more rows of lavender, each with the same number of plants at least 3 feet tall as the other rows of lavender. If a plant is now selected at random from the plants that are at least 3 feet tall, what is the probability that it is lavender?

Traps to Avoid

  • Using the grand total as the denominator on a conditional question instead of the total for the stated subgroup.
  • Reading a row total when the condition defines a column (or vice versa).
  • Computing P(A and B) when the question asks P(A given B).

Difficulty Progression

1. Foundation

Compute one-event probabilities from simple counts.

2. Developing

Read unions, intersections, and complements from tables or sample spaces.

3. Advanced

Select the correct restricted denominator for conditional questions with distracting totals.

Official taxonomy: College Board Math skills and question descriptions. Strategy and progression labels are Grind1600 editorial guidance. Last reviewed August 29, 2026.

Want more official questions for this skill?

The College Board Student Question Bank can filter official SAT questions by section, domain, skill, and difficulty. Read our question-bank workflow guide before choosing a set.

More Problem-Solving & Data Analysis Skills

Ratios, Rates & Units

Setting up proportions, converting units, and reasoning with rates — the most common word-problem machinery on the SAT Math section.

Percentages

Percent change, percent of a quantity, reverse-percentage problems, and multi-step percent scenarios like tax-plus-discount.

Data Distributions & Measures of Center

Mean, median, mode, range, and standard deviation — and how outliers or skew change them — read from lists, tables, and frequency plots.

Scatterplots & Two-Variable Data

Reading scatterplots, lines of best fit, interpreting slope in context, and distinguishing linear from exponential association.

Inference & Margin of Error

What sample results let you conclude about a population, how margin of error works, and why sample size changes confidence.

Evaluating Statistical Claims

Judging what a study design supports: random sampling vs. random assignment, causation vs. correlation, and generalizability.

Continue With Problem-Solving & Data Analysis Practice

Practice is sorted by domain and difficulty. On the Free plan you get the first 5 questions of each difficulty in Problem-Solving & Data Analysis. Pro opens every question in the bank.

Open the Question Bank

Want a schedule too? Preview a personalized study plan.

Last reviewed August 29, 2026 · Grind1600 Editorial Team