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4MA1/2FR Jan 2023, Question 12: Venn Diagrams

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

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The question, in short

Given 30 children, 5 with both a cat and a dog, 13 with a dog, and 11 with only a cat, complete the Venn diagram and find two probabilities for a randomly chosen child.

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

Part (a) · 3 marks

Complete the Venn diagram for sets C and D using the 30 children, 5 with both, 13 with a dog, and 11 with only a cat.

  1. 15 in the intersection of C and D
  2. 213 − 5 = 8 in D only
  3. 311 in C only
  4. 430 − (11 + 5 + 8) = 6 outside both circles

AnswerCat only: 11; cat and dog: 5; dog only: 8; outside both: 6

Part (bi) · 1 mark

Find the probability that a randomly chosen child has a dog.

  1. 1Total with a dog = 8 + 5 = 13
  2. 213 / 30

Answer13/30

Part (bii) · 1 mark

Find the probability that a randomly chosen child has neither a dog nor a cat.

  1. 16 children have neither cat nor dog
  2. 26 / 30

Answer6/30

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