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0580/31 May/Jun 2021, Question 9: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 6 marks

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The question, in short

Using ℰ = {1,...,12}, E = evens and M = multiples of 3, complete a Venn diagram, find n(E ∪ M), find a probability for E ∩ M, and judge Meg's claim about even primes.

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

Part (ai) · 2 marks

Place the numbers 1 to 12 into the correct regions of the Venn diagram for sets E and M.

  1. 1E = {2, 4, 6, 8, 10, 12}, M = {3, 6, 9, 12}
  2. 2E ∩ M: 6, 12
  3. 3E only: 2, 4, 8, 10 and M only: 3, 9
  4. 4Outside both circles: 1, 5, 7, 11

AnswerE only: 2, 4, 8, 10 E ∩ M: 6, 12 M only: 3, 9 Outside both circles: 1, 5, 7, 11

Part (aii) · 1 mark

State the number of elements in the union of E and M.

  1. 1E ∪ M = {2, 3, 4, 6, 8, 9, 10, 12}
  2. 2n(E ∪ M) = 8

Answer8

Part (aiii) · 2 marks

For a random pick from ℰ, give the probability of landing in both E and M.

  1. 1E ∩ M = even multiples of 3 = {6, 12}
  2. 2That is 2 numbers out of 12.
  3. 3P = 2/12 = 1/6

Answer1/6

Part (b) · 1 mark

Decide whether Meg is right that no even number is prime, giving a reason.

  1. 1No, 2 is even and a prime (its only factors are 1 and 2)

AnswerNo, 2 is even and a prime

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Also searched as: 0580/31/M/J/21 · 0580_s21_qp_31 · 0580 s21 31 · question 9.
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