SAT-Style: Probability from Two-Way Tables

SAT Math · Axiom Academy

SAT-Style Probability from Two-Way Tables Extract probabilities and conditional probabilities from frequency tables Problem 1: Extracting Conditional Probability A school surveyed 250 students about their morning commute: Question: What is the probability that a randomly selected student is a Freshman, given that they commute by bus? Step 1: Identify This as a Conditional Probability We need P(Freshman | Bus), which means we're looking at the "given that" condition (bus riders) and finding what fraction are freshmen. Step 3: Extract Values from Table Problem 2: Finding Simple Probability from Two-Way Table Question: If we randomly select a student from all 250, what is the probability they are a Junior who walks to school? Step 1: Identify This as Simple Probability We're selecting from all 250 students, so the denominator is the grand total. From the table: Juniors who walk = 10, Total = 250 Problem 3: Marginal vs. Conditional Probability Question A: What proportion of all students take the car to school? Question B: Among Seniors, what proportion take the car? Question A: Marginal Probability (Proportion of All) 46% of all students take the car. Question B: Conditional Probability (Among Seniors) Among Seniors, 66.7% take the car. Insight: Seniors are more likely to take the car (66.7%) than the general population (46%). This suggests an association between grade level and transportation choice. Axiom Academy SAT Prep | Unit 3: Problem Solving & Data Analysis

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