Problem Solving & Data Analysis • 15% of test
Probability
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Probability?
Probability measures the likelihood of events. The SAT tests basic probability, conditional probability, and probability from tables.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
What's the probability formula?
P(event) = number of favorable outcomes / total number of possible outcomes.
What's conditional probability?
The probability of A given that B has occurred. Written P(A|B). Restrict to B's outcomes only.
When do I add vs multiply probabilities?
Add for 'or' (either event). Multiply for 'and' (both events need to happen).
How do I read two-way tables for probability?
Identify the numerator (desired category) and denominator (relevant total) from the table.
What does 'at least one' mean?
It's easier to calculate P(at least one) = 1 - P(none). Use the complement.
Are probability questions hard?
Most SAT probability is straightforward. Focus on reading tables and identifying totals in our <a href='/math'>Math practice modules</a>.
What is 'Mutually Exclusive'?
Two events that cannot occur at the same time. Their intersection P(A and B) is zero.
What is the 'Complement' of an event?
The event NOT happening. P(Not A) = 1 - P(A). This is useful for 'at least one' problems.
How do I calculate probability without replacement?
Subtract 1 from the total denominator (and numerator if picking the same type) for each subsequent pick.
How do I use a 'Tree Diagram'?
Multiply along the branches to find the probability of a specific sequence of events happening.
What is 'Experimental' vs 'Theoretical' probability?
Theoretical is based on perfect logic (1/6 for a die). Experimental is based on actual trial data or observations.
How do I handle 'Expected Value'?
Multiply each possible outcome by its probability and sum them up. It represents the long-term average.
Does the SAT test 'Combinations'?
Rarely directly, but basic counting principles help you find the total possible outcomes for the denominator.
What is 'Independent' vs 'Dependent' probability?
Independent events don't affect each other (two coin flips). Dependent events do (drawing cards without replacement).
How do I find the probability of 'At Most One'?
Add the probability of zero and one event occurring. Master these basics in our <a href='/math/probability/beginner'>Beginner Probability sets</a>.