Construct and interpret two-way frequency tables as sample spaces for independence and conditional probability.
Complete a two-way frequency table, including all margins
Problem
Add the cells in the shown gender-and-response table to obtain \(\text{both}~\text{row}~\text{totals}\), \(\text{both}~\text{column}~\text{totals}\), and the grand total. Verify the margins sum to the same total.
A complete two-way table reconciles interior category counts with every row, column, and overall margin. We’ll sum across each response row, down each gender column, and then obtain the grand total in both directions. Agreement between the row-total sum and column-total sum verifies that every observation was counted once and placed consistently.
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