This topic summary covers Knowledge Organiser: Two-Way Tables within Two-Way Tables for GCSE Mathematics. Revise Two-Way Tables in Probability for GCSE Mathematics with 12 exam-style questions and 4 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Two-Way Tables
Key Terms
- Two-way table: A grid showing frequencies for two categorical variables
- Joint frequency: The count in a single cell (one specific row AND column)
- Marginal frequency: A row total or column total
- Grand total: The sum of all frequencies in the table
- Conditional probability: Probability given a specific row or column condition
- Relative frequency: A cell value divided by the grand total
Must-Know Facts
- Row totals and column totals must both sum to the grand total
- P(event) = frequency ÷ grand total for unconditional probability
- For P(A | B): use the relevant row or column total as the denominator
- "And" questions use the joint cell; "or" questions use marginal totals
- Always verify row totals and column totals match before calculating
- Missing values can be found by subtracting known cells from totals
Key Methods
- P(A and B) = joint frequency ÷ grand total
- P(A) = marginal frequency for A ÷ grand total
- P(A | B) = joint frequency for A and B ÷ marginal frequency for B
- Check: all row totals sum to grand total; all column totals sum to grand total
Key Formulas
- P(A and B) = cell frequency ÷ grand total
- P(A | B) = cell frequency ÷ row/column total for B
- P(A) = row/column total ÷ grand total
- Missing values: use row/column totals to find missing cells
Common Mistakes
- Wrong denominator for conditional probability: P(A|B) uses the B total as denominator — not the grand total
- Not completing the table first: Find all missing values using row/column totals before calculating any probabilities
- Misreading rows and columns: Clearly label which category is in rows and which in columns before reading off values
- Using grand total for P(A|B): Conditional probability restricts the sample space to B — use B's total not the overall total
Practice questions for Two-Way Tables
A two-way table shows information about 80 students. It shows whether they study French or Spanish, and whether they are in Year 10 or Year 11. The total number of Year 10 students who study French is the value found by looking at which intersection?
Explain why the denominator changes when finding conditional probability from a two-way table.