Venn Diagrams: Enumerating Sets (Year 8)
Free printable UK Year 8 (Key Stage 3) maths worksheet: use the 4 counts of a 2-set Venn diagram to enumerate outcomes and find probabilities.
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Grade 7 · Math worksheet
Name
Date
Math
Venn Diagrams: Enumerating Sets
Use the 4 counts of a 2-set Venn diagram (both, only 1 set, only the other, neither) to find each probability.
- 1.In a survey of 30 people: 7 like both football and rugby, 3 like only football, 15 like only rugby, and 5 like neither. Find P(a randomly chosen person likes football (including both)), giving your answer as a fraction in its simplest form.
- 2.In a survey of 50 people: 12 like both tea and coffee, 10 like only tea, 13 like only coffee, and 15 like neither. Find P(a randomly chosen person likes coffee (including both)), giving your answer as a fraction in its simplest form.
- 3.In a survey of 33 people: 5 like both swimming and cycling, 10 like only swimming, 10 like only cycling, and 8 like neither. Find P(a randomly chosen person likes neither swimming nor cycling), giving your answer as a fraction in its simplest form.
- 4.In a survey of 40 people: 13 like both tea and coffee, 11 like only tea, 10 like only coffee, and 6 like neither. Find P(a randomly chosen person likes exactly one of tea or coffee), giving your answer as a fraction in its simplest form.
- 5.In a survey of 19 people: 11 like both swimming and cycling, 3 like only swimming, 3 like only cycling, and 2 like neither. Find P(a randomly chosen person likes swimming (including both)), giving your answer as a fraction in its simplest form.
- 6.In a survey of 32 people: 12 like both football and rugby, 6 like only football, 12 like only rugby, and 2 like neither. Find P(a randomly chosen person likes rugby (including both)), giving your answer as a fraction in its simplest form.
- 7.In a survey of 22 people: 6 like both swimming and cycling, 7 like only swimming, 3 like only cycling, and 6 like neither. Find P(a randomly chosen person likes neither swimming nor cycling), giving your answer as a fraction in its simplest form.
- 8.In a survey of 34 people: 4 like both swimming and cycling, 6 like only swimming, 15 like only cycling, and 9 like neither. Find P(a randomly chosen person likes exactly one of swimming or cycling), giving your answer as a fraction in its simplest form.
- 9.In a survey of 32 people: 4 like both maths and art, 5 like only maths, 15 like only art, and 8 like neither. Find P(a randomly chosen person likes maths (including both)), giving your answer as a fraction in its simplest form.
- 10.In a survey of 31 people: 4 like both tea and coffee, 12 like only tea, 8 like only coffee, and 7 like neither. Find P(a randomly chosen person likes coffee (including both)), giving your answer as a fraction in its simplest form.
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