Determine event independence using P(A and B)=P(A)P(B).
Classify dependence and identify the decisive probability evidence
Problem
For \(\text{two}~\text{cards}\) drawn without replacement, compare \(P(\text{second}~\text{red}~|~\text{first}~\text{red})=25/51\) with \(P(\text{second}~\text{red})=1/2\) and classify the events.
Big Picture
What this problem is really about
A direct independence test compares a conditional probability with its unconditional counterpart. We’ll write both exact fractions, cross-multiply rather than rely on rounded decimals, interpret their inequality as a probability change caused by the first draw, and identify that change as the decisive evidence.
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