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4MA1/2H Jun 2024, Question 16: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

Use given counts of 60 art students choosing knitting, photography and embroidery to fill a three-set Venn diagram, then find probabilities and set counts.

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

Part (a) · 3 marks

Complete the Venn diagram with the number of students in each region using the given totals and overlaps.

  1. 1All three: 9.
  2. 2Exactly two: K and P 17 − 9 = 8; P and E 16 − 9 = 7; K and E 20 − 9 = 11.
  3. 3P only = 28 − (8 + 9 + 7) = 4; E only = 39 − (11 + 9 + 7) = 12.
  4. 460 − 2 = 58 chose at least one, so K only = 58 − (9 + 8 + 7 + 11 + 4 + 12) = 7.
  5. 5K only 7, P only 4, E only 12, KP 8, PE 7, KE 11, all 9, none 2

AnswerK only: 7; P only: 4; E only: 12; K and P only: 8; P and E only: 7; K and E only: 11; all three: 9; outside all three: 2

Part (b) · 2 marks

Given the chosen student chose photography, find the probability they also chose knitting.

  1. 1Given student chose photography, so sample space is 28
  2. 2Number who chose both photography and knitting = those in P ∩ K
  3. 3P ∩ K includes: (K ∩ P only) + (K ∩ P ∩ E) = 8 + 9 = 17
  4. 4So probability = 17 / 28

Answer17/28

Part (c) · 1 mark

Find n(P ∩ K′), the number choosing photography but not knitting.

  1. 1P ∩ K' means in photography but not in knitting
  2. 2Regions: (P only) + (P ∩ E only) = 4 + 7 = 11

Answer11

Part (d) · 1 mark

Find n([P ∪ E] ∩ K), the number choosing knitting and also photography or embroidery.

  1. 1[P ∪ E] ∩ K means in (photography or embroidery) and also in knitting
  2. 2So must be in K and also in P or E
  3. 3This includes: (K ∩ P only) + (K ∩ E only) + (K ∩ P ∩ E)
  4. 4= 8 + 11 + 9 = 28

Answer28

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