SAT probability questions sit inside Problem-Solving and Data Analysis on Digital SAT Math. College Board's assessment framework puts that domain at about 15% of Math, or 5 to 7 scored questions. Probability and conditional probability is one testing point in that domain, next to ratios, percentages, and data displays. The live set below is the artifact.
These are the same items as a Larry Learns problem-solving quiz: eight below, five per session in the app, then a streak. Cover the answers, finish the set, then read every explanation. Graphing moves live on SAT Desmos practice. Mixed math volume lives on SAT math practice questions.
How SAT Probability Questions Work
The official Math section page and the assessment framework name the skill as probability and conditional probability. You will see equally likely outcomes, "at random," two-step draws, and "given that." Math as a whole is 44 questions in 70 minutes, two 35-minute modules, per College Board's structure page.
College Board does not publish a standalone count for probability items. Treat this page as a skill drill, not a promise that every form has eight probability questions. You can see the four math domains on the SAT Math page.
SAT Probability Practice Questions With Answers
Each item uses the Digital SAT shape: a short setup, four choices. Reduce fractions. Cover the answers first.
1. Complement. A bag has 5 red, 3 blue, and 2 green marbles. One marble is drawn at random. What is the probability it is not green?
Answer: D. Ten marbles, eight are not green. 8/10 = 4/5. 1/5 is P(green). 2/5 counts only the blues as "not green."
2. At least one. A fair coin is flipped twice. What is the probability of at least one heads?
Answer: C. Four outcomes: HH, HT, TH, TT. Three have a heads. The complement is TT, which is 1/4, so 1 - 1/4 = 3/4. 1/2 counts only the mixed flips.
3. Simple event. A fair six-sided die is rolled. What is the probability the number is even?
Answer: C. Even faces are 2, 4, and 6. Three of six is 1/2. 1/3 is two faces. 2/3 is the odds of even, not the probability.
4. Two dice. Two fair six-sided dice are rolled. What is the probability the sum is 8?
- A) 1/12
- B) 5/36
- C) 1/6
- D) 1/4
Answer: B. Five pairs: (2,6), (3,5), (4,4), (5,3), (6,2). 5/36. 1/6 is the sum-7 count. 1/12 is 3/36, which drops two of the pairs.
5. Without replacement. A jar has 7 red marbles and 3 blue marbles. Two marbles are drawn at random, one after the other, without putting the first back. What is the probability both are blue?
- A) 1/15
- B) 1/10
- C) 9/100
- D) 3/10
Answer: A. First blue is 3/10. Second blue is 2/9. Product is 6/90 = 1/15. 9/100 treats the draws as independent with the first fraction squared. 3/10 is only the first draw.
6. Conditional. A club has 40 members. 24 ride the bus and 16 walk. Of the bus riders, 18 live more than two miles away. If a member is selected at random from those who ride the bus, what is the probability that member lives more than two miles away?
- A) 18/40
- B) 24/40
- C) 18/24
- D) 16/24
Answer: C. "Given that" shrinks the sample to the 24 bus riders. 18 of those 24 live more than two miles away. 18/24 = 3/4. 18/40 ignores the condition.
7. Independent. A spinner lands on red with probability 1/4. A fair coin is flipped. The spinner and the coin do not affect each other. What is the probability of red and heads?
Answer: A. Independent events multiply: (1/4)(1/2) = 1/8. 3/4 adds them. 1/4 is only the spinner.
8. Two-way table. A class of 30 students was asked whether they take Spanish, French, both, or neither. 18 take Spanish, 15 take French, and 9 take both. One student is selected at random. What is the probability the student takes Spanish or French?
- A) 9/30
- B) 18/30
- C) 24/30
- D) 33/30
Answer: C. Spanish or French is 18 + 15 - 9 = 24, so 24/30 = 4/5. Adding 18 and 15 without subtracting the overlap is 33/30, which is impossible. 9/30 is only "both."
Score yourself by family: complement, condition, without replacement, or. A 6 of 8 with two "given that" misses tells you what to drill next. For more volume in this format, start a free practice set or create a free account.
Probability Families the Digital SAT Actually Tests
The framework lists probability and conditional probability as one testing point under Problem-Solving and Data Analysis. The other points in that domain are ratios, percentages, one-variable data, two-variable data, inference, and evaluating statistical claims. Do not turn this page into a statistics course. Stay on the four families below.
| Family | Tell | Common trap |
|---|
| Complement | "Not," "at least one" | Counting the named event instead of 1 minus it |
| Condition | "Given that," "from those who" | Keeping the original denominator |
| Without replacement | Two draws, no put-back | Squaring the first fraction |
| Or | Two overlapping groups | Adding without subtracting the overlap |
Hard SAT Probability Questions
Hard items reuse easy words. "At least" is a complement in costume. "Given that" shrinks the bag. Two-step draws change the second denominator. If a choice is greater than 1, it added overlapping groups.
A calculator is allowed. It does not pick the sample space. Write the count before you divide. Desmos scientific mode can reduce a fraction. It cannot tell you that the condition changed the bag. Use math strategies for the rest of Problem-Solving and Data Analysis after these four families are clean.
Khan Academy and Worksheet Versions
Khan Academy's Official SAT Prep still drills Problem-Solving and Data Analysis. Use it for the lesson. Full-length Digital SAT tests live in Bluebook. A "probability worksheet" or PDF of the eight items above is this page. Print it if you want paper.
Larry Learns is the daily layer: three free quizzes a day, an explanation on every question, SAT and ACT in one account. Ace is $19 a month if you want the caps off. The SAT prep schedule template shows how to slot a short probability set into a longer week.
Frequently Asked Questions About SAT Probability Questions
How many probability questions are on the SAT?
College Board does not publish a standalone count. Problem-Solving and Data Analysis as a whole is about 5 to 7 scored questions, and probability is one testing point inside that domain.
What kinds of SAT probability questions show up?
Equally likely outcomes, complements, two-step draws without replacement, and conditional probability from a table or a "given that" sentence.
Are SAT probability questions calculator-active?
Yes. A calculator is allowed on every Math question. The hard step is still naming the sample space. Use Desmos for arithmetic, not for the story.
Where can I find hard SAT probability practice?
Hard items hide the complement and the condition. The eight questions above include both. Bluebook full-lengths add official volume.
Does Khan Academy have SAT probability questions?
Yes. Official SAT Prep covers Problem-Solving and Data Analysis. Full-length tests are in Bluebook. Use Khan for the lesson and a daily quiz for the habit.
What is the fastest way to improve on SAT probability questions?
Name the family before you compute: complement, condition, without replacement, or. Then write the counts. Short sets beat mixed marathons.
The eight questions above are a diagnostic. Once you know which family costs you the most, start a free practice set or create a free account to keep the streak on that family.
