Understand conditional probability and connect independence to unchanged conditional probabilities.
Judge whether a claim is supported by conditional probability information
Problem
Does this conditional probability information support the claim? Claim: club members are more likely to prefer math; \(P(\text{math}|\text{club})=0.70\) and \(P(\text{math}|\text{not}~\text{club})=0.45\)
Big Picture
What this problem is really about
A comparative claim is supported by conditional rates only when they measure the same outcome across the stated groups. We’ll align the outcome, compare the two group probabilities and their percentage-point difference, judge the association claim, and stop short of an unsupported causal conclusion.
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