Probability and Conditional Probability
Calculating probabilities, conditional probability, and working backwards
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You get a table or a scenario. The question asks: what's the probability?
Why this matters
Probability questions look simple — favorable over total, done. But the SAT makes you work for one or both of those numbers. There are four distinct question types, from basic lookup to conditional probability to working backward from a given probability. Each one has a different setup, and confusing them costs easy points.
The four patterns
Direct Probability
Favorable outcomes and total outcomes are right there. Find them, divide, done. The quickest points on the test.
›Two-Step Probability
Either the numerator or denominator isn't directly given. You need to add, subtract, or calculate before you can divide.
›Conditional Probability
Find the probability of an event given that another event already happened. Your denominator shrinks to just that subset.
›Working Backwards
You're told the probability and need to find a missing count. Set up the fraction equal to the given probability and solve.
The biggest trap: using the grand total as your denominator when the question says "given that…" That word given means you restrict to a row or column total. Miss it and you'll pick the wrong answer with full confidence.