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0580/22 Oct/Nov 2025, Question 12: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 6 marks

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The question, in short

Fitness club of 100 members: 60 swim, 70 cycle, 25 do neither. Use a Venn diagram to work out the overlap and region counts, then find three probabilities for a randomly chosen member.

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

Part (a) · 3 marks

Fill in the Venn diagram for the 100 members, placing the number who swim only, cycle only, do both, and neither.

  1. 1Number in S or C = 100 − 25 = 75
  2. 2S ∩ C = 60 + 70 − 75 = 55
  3. 3S only = 60 − 55 = 5, C only = 70 − 55 = 15, outside = 25

AnswerS only: 5 S ∩ C: 55 C only: 15 Outside both: 25 (or as probabilities 0.05, 0.55, 0.15, 0.25)

Part (bi) · 1 mark

Find the probability that a randomly chosen member cycles.

  1. 1P(C) = 70/100

Answer70/100

Part (bii) · 1 mark

Find the probability that a randomly chosen member both swims and cycles.

  1. 1P(S ∩ C) = 55/100

Answer55/100

Part (biii) · 1 mark

Find the probability that a randomly chosen member swims or does not cycle.

  1. 1S ∪ C′ = everything except C only
  2. 2P(S ∪ C′) = (5 + 55 + 25)/100 = 85/100

Answer85/100

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Also searched as: 0580/22/O/N/25 · 0580_w25_qp_22 · 0580 w25 22 · question 12.
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