Explain conditional probability and independence in everyday language and situations.
Verify unchanged likelihood under independence
Problem
For a fair die with \(A=\text{even}\) and \(B=\text{multiple}~\text{of}~3\), compute \(P(A)\) and \(P(A|B)\). Compare them to test independence.
Big Picture
What this problem is really about
The unchanged-likelihood test compares A’s overall probability with A’s probability inside B. We’ll list the fair-die outcomes, compute the even marginal, restrict the sample space to multiples of three, compute the even rate there, and interpret equality as independence.
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