Two-way tables

Task goals

• Read a two-way table (including its row/column totals) to answer "how many" comprehension questions about a specific cell or a whole row/column.
• Complete a missing cell in a two-way table using its row total or column total.
• Find the probability of a combined (AND / intersection) event from the grand total, and the probability of a single category regardless of the other variable.
• Find an informal conditional ("given") probability by dividing a cell by its own row's or column's total, not the grand total, and compare conditional rates across two or more groups.
• Find an OR (union) probability, either by adding then subtracting the overlap (inclusion-exclusion) or by counting/subtracting a "neither" complement directly.
• Explain why a conditional probability P(A given B) is not generally equal to its reverse P(B given A), and why row and column totals must both agree with the grand total.