Probability on the SAT
Simple, Compound, and Complement
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Probability
Probability questions are really counting questions. The SAT gives you a situation and asks how likely a certain outcome is, which depends on how you count the total outcomes and the favorable ones.
This lesson shows the basic probability formula, how to decide whether events are independent or dependent, and how to avoid double counting. You will also practice interpreting the wording so you build the correct fraction.
A Simple Definition Unlocks Probability
Probability is favorable outcomes divided by total outcomes. If events are independent, you multiply their probabilities. If they are dependent, you adjust the denominator after each outcome.
A quick check is to make sure your probability is between $0$ and $1$. If your calculation gives a number outside that range, your counting method needs to be revised.
Work Through Probability Step by Step
What is the probability of two heads when flipping two coins?
Use a simple example to show how independent probabilities multiply step by step.
Each coin flip is independent
Multiply the probabilities because the events are independent.
Simplify the expression to make the next step clear.
Use Desmos to Check Probability
Compute $(3/5) \cdot (2/4)$ to model a without-replacement probability.
Desmos can calculate fractions quickly and is helpful for checking compound probabilities with many steps.
(3/5) * (2/4)
Algebra is usually faster for simple events. Desmos helps avoid arithmetic mistakes.
Desmos is faster for the arithmetic once you have the right fraction. The counting and reasoning are still algebraic and usually faster to do on paper.
Expert move: Use Desmos to crunch the arithmetic once you set up the correct probability model; it will not choose the model for you.
- Desmos features used: numeric evaluation.
- Common mistake: forgetting to adjust for without replacement.
Practice Probability with SAT-Style Questions
Compute probabilities carefully.
A bag has red and blue marbles. What is the probability of choosing a red marble?
Two coins are flipped. What is the probability of two heads?
A card is drawn from a standard deck. What is the probability it is NOT a heart?
A bag has green and yellow marbles. Two marbles are drawn without replacement. What is the probability both are green?
Key Takeaways to Remember for Probability
- Probability is favorable outcomes divided by total outcomes.
- Independent events multiply, dependent events adjust after each draw.
- Use the complement rule for "not" probabilities.
