SAT Math
Probability
Probability is a skill in the Problem-Solving and Data Analysis domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
Of the 200 students surveyed at a school, 120 said they play a school sport and 80 said they do not. Of the 120 students who play a sport, 45 also play a musical instrument. Of the 80 students who do not play a sport, 20 play a musical instrument. If a student who plays a sport is selected at random from those surveyed, what is the probability that this student also plays a musical instrument?
- A. 45/200
- B. 45/120 ✓
- C. 20/80
- D. 65/200
Correct answer: B. Since the selection is limited to students who play a sport, the relevant total is 120, and 45 of those students also play an instrument, giving a probability of 45/120.
A vending machine dispenses a random snack and a random drink with each purchase. The probability that the snack is pretzels is 0.4, and, independently, the probability that the drink is water is 0.35. What is the probability that a purchase results in both pretzels and water?
- A. 0.26
- B. 0.86
- C. 0.14 ✓
- D. 0.75
Correct answer: C. For independent events, the probability of both occurring is the product of their individual probabilities: 0.4 × 0.35 = 0.14.
A certain vaccine is 90% effective, meaning each vaccinated person has a 0.9 probability of being immune after a single dose. If 3 people are vaccinated independently, what is the probability that at least one of them is NOT immune?
- A. 0.1
- B. 0.3
- C. 0.729
- D. 0.271 ✓
Correct answer: D. The probability all 3 people are immune is 0.9³ = 0.729, so the probability that at least one is not immune is the complement, 1 − 0.729 = 0.271.
Among 200 students surveyed, 120 own a car and 80 do not. Of the car owners, 45 also own a bike. Of the students who do not own a car, 20 own a bike. If a student who owns a bike is selected at random, what is the probability that this student also owns a car?
- A. 9/13 ✓
- B. 45/120
- C. 45/200
- D. 20/65
Correct answer: A. Correct — a total of 45 + 20 = 65 students own a bike; of those, 45 also own a car, so the conditional probability is 45/65 = 9/13.
A factory tests a component that has a 10% chance of failing, independent of any other component. If three of these components are installed in a machine, what is the probability that at least one of them fails?
- A. 0.3
- B. 0.271 ✓
- C. 0.1
- D. 0.729
Correct answer: B. Correct — the probability that none of the three components fail is 0.9³ = 0.729, so the probability that at least one fails is 1 − 0.729 = 0.271.