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4MA1/2F Nov 2021, Question 15: Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2F (Foundation) · Calculator · 5 marks

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The question, in short

Given sets ℰ, X and Y, complete a Venn diagram and find the probability that a randomly chosen number from ℰ lies in X ∪ Y.

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

Part (a) · 3 marks

Place the elements of X and Y in the correct regions of the Venn diagram, including those outside both sets.

  1. 112 is in X and in Y, so 12 goes in the overlap
  2. 2X = {4, 8, 12, 16}, so 4, 8 and 16 go in X only
  3. 3Y = {6, 12, 18}, so 6 and 18 go in Y only
  4. 4The remaining members of E, 2, 10 and 14, go outside both circles
  5. 5Venn diagram: X only 4, 8, 16; overlap 12; Y only 6, 18; outside 2, 10, 14

AnswerX only: 4, 8, 16; X and Y: 12; Y only: 6, 18; outside both: 2, 10, 14

Part (b) · 2 marks

Find the probability that a number chosen at random from ℰ is in X ∪ Y.

  1. 1Count total numbers in E: 9
  2. 2Count numbers in X ∪ Y: 4, 6, 8, 12, 16, 18 → 6 numbers
  3. 3Probability = 6 / 9

Answer6/9

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