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
Complete the displayed grade-and-tea table by summing each grade row, each tea column, and the grand total. Check that \(\text{both}~\text{margin}~\text{sums}\) agree.
Completing a two-way table requires each margin to stay attached to the cells it summarizes. We’ll add across every row, add down every column, compute the grand total from both margin directions, and use agreement of those two totals to audit all entries.
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