Venn diagrams, events and two-way tables
Sort a class of 30 by football and chess in a Venn diagram, flip the same data into a two-way table and back, see events as sets and work out "or" probabilities with the addition rule.
- UK: Year 9
- France: grade 10
- Germany: grade 8
- Iran: grade 9
- Afghanistan: grade 9
- Syria: grade 9
- Palestine: grade 7
- Russia: grade 8
Guide
This studio follows KS3 "enumerate sets and combinations of sets systematically, using tables, grids and Venn diagrams" and GCSE probability (P6–P8). Iran teaches it in Year 9 («مجموعهها و احتمال») and Afghanistan in Year 9.
The universal set ξ (the sample space) is the whole class of 30, and every event is a subset of it: "football or chess" is F ∪ C, "both" is F ∩ C, "not chess" is C′. For "or" when the events overlap: P(A∪B) = P(A) + P(B) − P(A∩B); when they are mutually exclusive (no overlap), just add.
Common mistakes this studio works on: adding n(A) + n(B) when the sets overlap, mixing up "only football" and "football", forgetting the region outside the circles, and tables whose totals don't match.