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0580/12 Oct/Nov 2022, Question 17: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Use set data for 120 people with bicycle and car ownership to fill a Venn diagram, find a probability, and shade a union region.

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

Part (ai) · 2 marks

Complete the two-circle Venn diagram for sets B and C using 120 people, 21 bicycle owners, 15 with both, and 35 with neither.

  1. 1B only = 21 − 15 = 6; B ∩ C = 15
  2. 2C only = 120 − 35 − 21 = 64; outside both = 35

AnswerB only: 6; B ∩ C: 15; C only: 64; outside B and C: 35

Part (aii) · 1 mark

For a randomly chosen person, find the probability that they own a car.

  1. 1Own a bicycle or a car = 120 − 35 = 85
  2. 2Own a car only = 85 − 21 = 64
  3. 3Own a car = 64 + 15 = 79
  4. 4P(owns a car) = 79/120

Answer79/120

Part (b) · 1 mark

On the Venn diagram with sets D and E, shade the region representing D union E.

  1. 1Shade everything inside circle D or circle E (including the overlap), nothing outside them

AnswerBoth circles D and E fully shaded (the whole of D ∪ E); nothing outside them shaded

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Also searched as: 0580/12/O/N/22 · 0580_w22_qp_12 · 0580 w22 12 · question 17.
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