Reading a Venn diagram
A Venn diagram sorts things into two overlapping circles inside a box.
| Part of the diagram | Means | Here |
|---|---|---|
| Left circle only | football but not hockey | 8 |
| The overlap | both football and hockey | 3 |
| Right circle only | hockey but not football | 6 |
| Outside both circles | neither | 5 |
Counting from a Venn diagram
- Everyone who plays football = left only + overlap = 8 + 3 = 11
- Total = all four numbers added = 8 + 3 + 6 + 5 = 22
- Neither (when it’s missing) = total − the three numbers inside the circles
Probability from a Venn diagram
P(a pupil picked at random plays both) = both ÷ total = 3/22
Watch out! “Plays football” means the whole football circle, including the overlap. “Plays only football” means just the part that doesn’t overlap.
Top tip: when a question gives you the total, check that all four numbers add up to it.
⭕ Number sort1 of 10
Where does 2 go? Tap the diagram.
🎮 Pets surveyQuestion 1 of 5