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4MA1/1H Nov 2021, Question 16: Three-Set Venn Diagrams

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

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The question, in short

Given 32 students' pass counts for Maths, English and French plus overlaps and 4 failing all, use the Venn diagram to find x, complete the diagram, and find a probability.

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

Part (a) · 2 marks

Using the Maths pass total of 25 and the given overlaps, form an equation to find x.

  1. 1M and E only = 18 − x; M and F only = 11 − x; M only = 3
  2. 2Maths total: 3 + (18 − x) + x + (11 − x) = 25
  3. 332 − x = 25, so x = 7

Answer7

Part (b) · 2 marks

With the found x, fill every region of the Venn diagram with student counts.

  1. 1M and E only = 18 − 7 = 11; M and F only = 11 − 7 = 4; centre = 7
  2. 2E only = 20 − 11 − 7 − 2 = 0
  3. 3F only = 14 − 4 − 7 − 2 = 1
  4. 4Outside = 4; check 3 + 11 + 7 + 4 + 0 + 2 + 1 + 4 = 32

AnswerM only 3, M and E only 11, all three 7, M and F only 4, E only 0, E and F only 2, F only 1, outside all three 4

Part (c) · 1 mark

For a randomly chosen Maths passer, find the probability they failed French.

  1. 125 students passed Maths
  2. 2Of these, failed French: M only 3 + M and E only 11 = 14
  3. 3Probability = 14/25

Answer14/25

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