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How is conditional probability calculated from a two-way contingency table on the SAT?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

$P(A|B) = \frac{\text{Number in category } A \text{ and } B}{\text{Total in condition category } B}$. Restrict your denominator strictly to the given condition group, not the grand total.

Explanation

Phrases like 'Given that the person is in group B...' or 'Of those who tested positive...' signal that the total sample space is restricted to group B.

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