Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Complete a column-relative-frequency table
Problem
For columns \((12,8)\) and \((10,20)\), divide entries by column totals \(20\) and \(30\). Reduce the column-relative frequencies and verify each column sums to \(1\).
Column-relative frequencies normalize each column independently. We’ll divide the upper and lower cells by their own column margin, reduce both columns’ fractions, and use a sum of one within each column to audit the completed distributions.
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