SAT Math: SAT Math: Probability Practice Questions
Test yourself on SAT Math: Probability with 10 original SAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of SAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue?
Explanation. Total marbles = 5 + 3 + 2 = 10. Non-blue marbles = 5 + 2 = 7. So P(not blue) = 7/10. Subtracting blue from the total is the key step.
2. A standard six-sided die is rolled once. What is the probability of rolling an even number greater than 2?
Explanation. Even numbers greater than 2 are 4 and 6, giving 2 favorable outcomes out of 6 total. P = 2/6 = 1/3. A common error is counting 2 itself, but it is not greater than 2.
3. In a survey of 200 students, 120 play a sport and 80 do not. If one student is chosen at random, what is the probability that the student does NOT play a sport?
Explanation. Students who don't play = 80 out of 200. P = 80/200 = 2/5. Always identify the favorable group and divide by the total.
4. A jar has 12 candies: 4 cherry, 5 lemon, and 3 grape. Two candies are drawn without replacement. What is the probability that both are lemon?
Explanation. P(first lemon) = 5/12. After removing one lemon, P(second lemon) = 4/11. Multiply: (5/12)(4/11) = 20/132 = 5/33. Without replacement means the second probability uses reduced counts.
5. A spinner is divided into 8 equal sections numbered 1 through 8. What is the probability of landing on a prime number?
Explanation. Primes from 1 to 8 are 2, 3, 5, and 7 — four numbers. P = 4/8 = 1/2. Note that 1 is not prime, which trips up many students.
6. The table shows 150 people surveyed by age and preference. 90 prefer coffee and 60 prefer tea. Of the coffee drinkers, 30 are under 30 years old. If a coffee drinker is selected at random, what is the probability the person is under 30?
Explanation. This is conditional probability: we restrict to the 90 coffee drinkers. Of those, 30 are under 30. P = 30/90 = 1/3. The total of 150 is irrelevant since we condition on coffee drinkers.
7. Two fair coins are flipped. What is the probability of getting at least one head?
Explanation. The outcomes are HH, HT, TH, TT. 'At least one head' is everything except TT, so 3 of 4 outcomes. P = 3/4. Using the complement P(at least one head) = 1 − P(no heads) = 1 − 1/4 = 3/4 is the fastest method.
8. A box contains 6 defective and 14 non-defective parts. If two parts are selected without replacement, what is the probability that the first is defective and the second is non-defective?
Explanation. P(first defective) = 6/20 = 3/10. After removing it, 19 remain with 14 non-defective, so P(second non-defective) = 14/19. Multiply: (3/10)(14/19) = 42/190 = 21/95.
9. A class has 18 girls and 12 boys. The probability of randomly selecting a girl is what fraction?
Explanation. Total = 18 + 12 = 30. P(girl) = 18/30 = 3/5. Reduce the fraction by dividing numerator and denominator by 6.
10. In a deck of cards, 40% of cards are blue and the rest are yellow. Among blue cards, 25% have a star. If a card is drawn at random, what is the probability it is a blue card with a star?
Explanation. P(blue and star) = P(blue) × P(star given blue) = 0.40 × 0.25 = 0.10. This multiplies the chance of being blue by the conditional chance of having a star.
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FAQ
Do I need to memorize probability formulas for the SAT?
You mainly need the basic idea: probability = favorable outcomes ÷ total outcomes. For 'and' events without replacement, multiply probabilities while adjusting counts; for 'at least one' situations, the complement (1 − P) is often fastest. The SAT rarely requires advanced formulas like permutations.
How do SAT probability questions usually present data?
Often through two-way frequency tables, word descriptions of bags/spinners/dice, or survey results. Read carefully to identify whether you want the whole group as the denominator or a restricted subgroup (conditional probability).
What's the most common mistake on SAT probability problems?
Using the wrong total. In conditional probability ('given that...'), you divide by the subgroup size, not the overall total. Also watch for 'without replacement,' where the second draw's denominator decreases by one.