Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Decide whether two variables are independent by comparing a marginal probability to a conditional probability
Problem
Use conditional probabilities to decide whether the variables are independent: \(P(A)=0.40\) and \(P(A|B)=0.40\).
Big Picture
What this problem is really about
A conditional independence test asks whether restricting to B changes A’s rate. We’ll compare the conditional probability directly with A’s marginal probability, measure their difference, and interpret exact equality as no change rather than adding or reversing the quantities.
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