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Data Analysis · Skill 5 of 7

SAT Probability Practice

SAT probability is not poker hands and dice chains. On the digital SAT it is almost entirely counting from two way tables and handling one phrase, given that, with precision. This page shows the patterns, conditions one table completely, then gives you drills that build a fresh table every time.

  • Domain: Data Analysis
  • About 15% of the test is Data Analysis
  • Difficulty: easy to hard
  • Free, no account
Drill probability now → See all Data Analysis skills

The patterns the SAT actually uses

Every SAT probability question is a favorable count over a total count. The four patterns differ only in which counts you are allowed to use.

Pattern 01

One cell over the grand total

The probability that a person chosen from everyone surveyed lands in one cell. Read the cell, divide by the number in the corner of the table, done.

Pattern 02

Condition on a row or column

Given that the person is in one group, the denominator becomes that group's total. The grand total leaves the problem entirely, and choices built on it are traps.

Pattern 03

Build the table first

Hard versions describe the counts in prose. Sketch the two way table, fill in the margins, and the actual probability question collapses into a single division.

Pattern 04

Complements and at least

The probability something does not happen is 1 minus the probability it does. Questions with at least one almost always run faster through the complement.

One worked example, start to finish

Worked example · medium

A survey asked 200 students whether they prefer classes in person or online. Of the 90 juniors surveyed, 60 prefer in person and 30 prefer online. Of the 110 seniors surveyed, 70 prefer in person and 40 prefer online. If one of the surveyed seniors is chosen at random, what is the probability that the chosen student prefers online classes?

  1. The condition does the sorting: the student is chosen from the seniors, so the denominator is the 110 seniors, not all 200 students.
  2. Count the favorable cell: seniors who prefer online classes, which is 40.
  3. Divide: 40/110 = 4/11.
  4. Check the table totals: 60 + 30 = 90 juniors, 70 + 40 = 110 seniors, and 90 + 110 = 200 students. Everything is consistent, and 4/11 ≈ 0.36 is a sensible probability.

Answer: 4/11

Regenerated versions swap juniors and seniors for pets and playlists. The condition always picks the denominator.

Where students lose the point

  • Keeping the grand total. Once the question chooses from one group, 200 is dead. The denominator is that group's total, 110 here, and the choice built on 40/200 is sitting right there.
  • Flipping the condition. The probability that a senior prefers online, 40/110, is not the probability that an online preferring student is a senior, 40/70. Decide which group is fixed before dividing.
  • Adding overlapping cells. Senior and online is one cell, 40. Adding the whole senior row to the whole online column counts that cell twice, and the inflated fraction is always offered.
  • Brute forcing at least one. Adding every qualifying case invites arithmetic slips. One minus the probability of none is shorter and safer, and hard questions are written assuming you know it.

Using Desmos here

Desmos plays a small role in this skill: it reduces fractions and turns 40/110 into a decimal for matching against answer choices. The real work, finding the conditioned group and the favorable cell, happens in the table itself, and no calculator reads a table for you. Practice until the phrase given that moves your eyes to the correct row on its own.

Why drilling here is different

Our probability drills generate a new table every single time: new categories, new counts, new conditions, at easy, medium, and hard difficulty. You cannot memorize your way through, which is the point. The conditioning move becomes automatic, and every answer in Satified's bank of 1,483 questions has been independently verified.

A fresh table, every time.

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Questions students ask

What does the phrase given that do to a probability question?
It shrinks your world. Given that the student is a senior means your denominator is only the seniors, not everyone surveyed. Locating that smaller group in the table is usually the entire question.
Should I answer with a fraction or a decimal?
Either works. Multiple choice questions show one form, and student produced responses accept any equivalent, so 4/11 and .3636 both earn credit. Fractions read straight from the table are faster and avoid rounding mistakes.
Do I need combinations or permutations?
No. SAT probability never requires counting formulas. Every question reduces to a favorable count divided by a total count, almost always read from a table, a list, or a short description.
How many probability questions are on the test?
Usually 1 to 2 of the 44 questions, inside the Data Analysis domain at about 15 percent of SAT Math. They cluster at medium difficulty, which makes them very winnable points.
Why do the tables change every time I practice?
Satified questions are generators. New counts, new categories, and new conditions load each time, so you learn to find the conditioned group anywhere instead of memorizing one table. It is free, with no account.

Keep going

Table reading and careful wording carry straight into inference and statistical claims, the final two skills of this domain.