Lemmara logoLemmaraWorked solution

0580/11 May/Jun 2026, Question 15: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 11 (Core) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use survey data on 60 people, with 41 liking reading, 31 liking cookery and 11 liking neither, to complete a Venn diagram, find a probability, and shade a set region.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Complete the two-set Venn diagram for R and C using the 60 people and the given counts.

  1. 1In R or C: 60 − 11 = 49
  2. 2Both: 41 + 31 − 49 = 23
  3. 3R only = 41 − 23 = 18, C only = 31 − 23 = 8, outside = 11

AnswerR only 18, R ∩ C 23, C only 8, outside 11

Part (aii) · 1 mark

For a randomly chosen person from the 60, find the probability of liking cookery but not reading.

  1. 1Like R or C: 60 − 11 = 49
  2. 2Like both: 41 + 31 − 49 = 23
  3. 3Cookery but not reading: 31 − 23 = 8
  4. 4P = 8/60

Answer8/60

Part (b) · 1 mark

On the given Venn diagram with sets A and B, shade the region for A ∩ B.

  1. 1A ∩ B means in both A and B
  2. 2Shade only the region where the two circles overlap

AnswerThe overlap of A and B shaded

Stuck on a step? Read the free lesson: Venn Diagrams

Practise more venn diagrams questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on venn diagrams

Also searched as: 0580/11/M/J/26 · 0580_s26_qp_11 · 0580 s26 11 · question 15.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.