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4MA1/2H Jun 2025, Question 20: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Use survey data on 120 gardeners growing carrots, potatoes and tomatoes to complete a Venn diagram, find a set count, and calculate a conditional probability.

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

Part (a) · 3 marks

Fill in the three-circle Venn diagram with the given counts, using the equal numbers growing only potatoes and only tomatoes.

  1. 1Centre (C∩P∩T) = 12
  2. 2C and P only = 18 − 12 = 6; C and T only = 27 − 12 = 15; P and T only = 32 − 12 = 20
  3. 3C only = 43 − 12 − 6 − 15 = 10
  4. 4Outside = 29
  5. 5P only + T only = 120 − 29 − 10 − 6 − 15 − 12 − 20 = 28
  6. 6P only = T only = 28 ÷ 2 = 14

AnswerC only 10, C and P only 6, P only 14, C and T only 15, all three 12, P and T only 20, T only 14, outside 29

Part (b) · 1 mark

Find the number of gardeners in T′ ∩ C, i.e. growing carrots but not tomatoes.

  1. 1T′ ∩ C: in C but not in T
  2. 2C only + (C and P only) = 10 + 6
  3. 3= 16

Answer16

Part (c) · 2 marks

Given a gardener grows carrots, calculate the probability they also grow potatoes.

  1. 1Gardeners who grow carrots = 43
  2. 2Of these, those who also grow potatoes = 6 + 12 = 18
  3. 3Probability = 18/43

Answer18/43

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