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4MA1/1FR Jan 2021, Question 14: Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 5 marks

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The question, in short

Given ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}, complete a Venn diagram and find a probability.

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

Part (a) · 3 marks

Place the elements of ℰ into the Venn diagram showing sets A and B, including the region outside both circles.

  1. 1Place 6 and 12 in the intersection of A and B
  2. 2Place 2, 4, 8, 10 in A only
  3. 3Place 3, 9 in B only
  4. 4Place 1, 5, 7, 11 in E but outside A and B

AnswerA only: 2, 4, 8, 10; A and B: 6, 12; B only: 3, 9; outside both: 1, 5, 7, 11

Part (b) · 2 marks

A number from ℰ is picked at random; find the probability it lies in neither A nor B.

  1. 1Count numbers not in A and not in B: 1, 5, 7, 11
  2. 2There are 4 such numbers
  3. 3Total numbers in E is 12
  4. 4Probability = 4/12

Answer4/12

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