Conditional count table
Compare a subgroup probability with a reversed condition.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 1–4 with adult support
- Time
- 15–25 minutes
- Materials
- A100-object two-way table
Prepare
Use a fictional collection of 100 paper objects:10 triangles and 90 circles. A fictional marker labels 8 triangles and 9 circles as flagged. The unflagged counts are 2 triangles and 81 circles. These are stipulated counts, not collected observations or a real diagnostic test.
Play
Fill a table with rows triangle/circle and columns flagged/unflagged. Compute row totals 10,90; column totals 17,83; grand total 100. Every object belongs in exactly one cell.
Worked example
Among flagged objects,8 of 17 are triangles, so the conditional fraction is 8/17. Among triangles,8 of 10 are flagged, so the reversed fraction is 8/10. The same numerator does not make the two questions equal.
Finish and check
Cover the unflagged column when answering “triangle given flagged”. Cover the circle row for “flagged given triangle”. A partner names the selected denominator before calculating. Use exact fractions rather than rounding to a whole object.
Adaptation and limits
Finish when the four cells and all margins add correctly and both conditions are explained. This fictional paper example is not medical guidance, a measured accuracy claim or a prediction about real people.
Purpose, observation and provenance
Within this activity: Compare a subgroup probability with a reversed condition.
Ask for the condition’s denominator before accepting either probability fraction.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
OpenStax: Contingency Tables — Reference supports the stated concept; our fictional numbers, instructions and paper diagrams are independently prepared, not reproduced teaching pages.
Secondary practice: Cooperation and explaining a check.
For a class of 30, use ten groups of three. Prepare one player-material set per group and keep the host key with the adult. Rotate operator, recorder and checker after each worked example; a reader or scribe may help without choosing answers. Avoid public ranking or diagnostic labels.
Age bands are planning suggestions. Background references may address older learners and do not validate suitability for this age band. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Rules to keep beside the materials
- Use a fictional collection of 100 paper objects:10 triangles and 90 circles. A fictional marker labels 8 triangles and 9 circles as flagged. The unflagged counts are 2 triangles and 81 circles. These are stipulated counts, not collected observations or a real diagnostic test.
- Fill a table with rows triangle/circle and columns flagged/unflagged. Compute row totals 10,90; column totals 17,83; grand total 100. Every object belongs in exactly one cell.
- Among flagged objects,8 of 17 are triangles, so the conditional fraction is 8/17. Among triangles,8 of 10 are flagged, so the reversed fraction is 8/10. The same numerator does not make the two questions equal.
- Cover the unflagged column when answering “triangle given flagged”. Cover the circle row for “flagged given triangle”. A partner names the selected denominator before calculating. Use exact fractions rather than rounding to a whole object.
- Finish when the four cells and all margins add correctly and both conditions are explained. This fictional paper example is not medical guidance, a measured accuracy claim or a prediction about real people.
Conditional count table — player materials
| Objects | Flagged | Unflagged | Total |
|---|---|---|---|
| Triangle | 8 | 2 | |
| Circle | 9 | 81 | |
| Total |
| Question | Numerator | Condition denominator | Fraction |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host check — keep separate
Cells 8,2,9,81; P(triangle|flag)=8/17, P(flag|triangle)=8/10.
Examples are stipulated model cases, not measured experimental or learning outcomes.