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4MA1/1H Jun 2018, Question 4: Probability with Venn Diagrams

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

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The question, in short

Use the Venn diagram with sets A, B, C to list set members, judge a statement about A ∩ C, and find a probability for C′.

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

Part (ai) · 1 mark

List all numbers inside circle A, including those shared with B.

  1. 1Identify all numbers inside circle A: 1, 2, 3, 4, 6, 12

Answer1, 2, 3, 4, 6, 12

Part (aii) · 1 mark

List all numbers in B or C or both, combining their regions.

  1. 1Identify all numbers in circle B or circle C: 1, 3, 5, 7, 9, 10, 11

Answer1, 3, 5, 7, 9, 10, 11

Part (b) · 1 mark

Decide whether A ∩ C = ∅ is true, giving a reason from the diagram.

  1. 1Check for any numbers common to both A and C
  2. 2No numbers appear in both A and C
  3. 3Therefore A ∩ C = Ø is correct

AnswerYes, because no number is in both A and C, so the sets do not overlap

Part (c) · 2 marks

Find the probability a randomly chosen number lies outside set C.

  1. 1There are 12 numbers in the diagram
  2. 2Only 5 and 10 are in C, so 12 − 2 = 10 numbers are in C′
  3. 3P(C′) = 10/12

Answer10/12

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