Basic Probability SAT — SAT Math Guide
Basic probability SAT questions test your ability to calculate the likelihood of events occurring. These problems involve finding the chances of outcomes in situations like coin flips, card draws, or survey results. You'll encounter 2-3 probability questions in the Problem Solving and Data Analysis domain on the Digital SAT. With the right approach, these can be some of your most reliable points on test day.
What You Need to Know
Probability = Number of favorable outcomes ÷ Total number of possible outcomes
All probabilities fall between 0 and 1 (or 0% and 100%)
The sum of all possible outcomes always equals 1
Independent events don't affect each other (coin flips)
Dependent events do affect each other (drawing cards without replacement)
"And" means multiply probabilities; "or" means add probabilities (for mutually exclusive events)
📐 KEY FORMULA: P(event) = favorable outcomes / total outcomes
💡 PRO TIP: Always check if your probability answer is between 0 and 1. If not, you made an error.
How to Solve Basic Probability on the SAT
Example Question 1 — Medium Difficulty
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 either red or green?
A) 0.3
B) 0.5
C) 0.7
D) 0.8
Solution:
Step 1: Count total marbles: 5 + 3 + 2 = 10 marbles
Step 2: Count favorable outcomes (red or green): 5 + 2 = 7 marbles
Step 3: Calculate probability: 7/10 = 0.7
✅Answer: C — The probability of drawing either red or green is 7 out of 10, which equals 0.7.
Example Question 2 — Hard Difficulty
In a class of 30 students, 18 play soccer, 12 play basketball, and 6 play both sports. If a student is chosen at random, what is the probability that the student plays soccer but not basketball?
A) 0.2
B) 0.4
C) 0.5
D) 0.6
Solution:
Step 1: Find students who play only soccer: 18 - 6 = 12 students
Step 2: Total students = 30
Step 3: Calculate probability: 12/30 = 2/5 = 0.4
✅Answer: B — Students who play soccer but not basketball make up 12 of the 30 students, giving us 0.4.
Common SAT Math Mistakes to Avoid
❌Mistake: Forgetting to subtract overlapping groups in "but not" problems
✅Fix: Always identify what's included in both categories first
❌Mistake: Adding probabilities when you should multiply (for "and" situations)
✅Fix: Remember "and" means multiply, "or" means add (for mutually exclusive events)
❌Mistake: Using the wrong total when calculating probability
✅Fix: Double-check what the denominator should be based on the question
❌Mistake: Converting fractions incorrectly to decimals
✅Fix: Use your calculator to verify decimal conversions
Practice Question — Try It Yourself
A spinner has 8 equal sections: 3 red, 3 blue, and 2 yellow. What is the probability of spinning red on the first spin AND blue on the second spin?
A) 3/32
B) 9/64
C) 6/64
D) 3/8
Show Answer
Answer: B — P(red then blue) = (3/8) × (3/8) = 9/64. Since the spins are independent, we multiply the individual probabilities.
Key Takeaways for the SAT
Always identify total possible outcomes before calculating probability
Remember that SAT math basic probability questions often involve real-world scenarios
Check if events are independent or dependent to decide whether to use replacement
Convert your final answer to match the format of the answer choices
Practice reading carefully to distinguish between "and" vs "or" probability questions
Related SAT Math Topics
Strengthen your SAT math prep with these related topics:
Data interpretation →
Statistics →