SAT Math: Two-Way Tables and Probability
35+ practice questions in Praczo
The concept, explained
- 1
A two-way table displays frequencies across two categorical variables. Rows = one variable, columns = another, cells = counts at each intersection.
- 2
Basic probability: P(event) = favorable outcomes / total relevant outcomes. Know which total to use — the grand total or a row/column subtotal.
- 3
Conditional probability ("given that..."): restrict your universe to the row or column that satisfies the condition, then find the proportion within it.
- 4
Marginal totals (row and column sums at the edges) are used for simple probabilities. Individual cells are used for joint probabilities.
- 5
"Given that" language signals conditional probability — use the row or column subtotal as your denominator, not the grand total.
- ✗ Using the grand total when the problem says "given that [condition]." Conditional probability requires the relevant subtotal as denominator.
- ✗ Confusing P(A and B) with P(A | B). The first uses the grand total; the second uses the total for B.
SAT-style practice
In a survey, 72 students who studied passed a test, 8 students who studied failed, 18 students who did not study passed, and 22 who did not study failed. A student who passed is selected at random. What is the probability the student studied?
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