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4MA1/2HR Jan 2021, Question 16: Venn Diagrams

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

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The question, in short

Sets with n(A) = 62, n(B) = 30, n(A ∪ B) = 68 out of 80: complete a two-set Venn diagram and find two probabilities from it.

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

Part (a) · 2 marks

Find each region's number.

  1. 1n(A ∩ B) = n(A) + n(B) − n(A ∪ B) = 62 + 30 − 68 = 24
  2. 2n(A only) = n(A) − n(A ∩ B) = 62 − 24 = 38
  3. 3n(B only) = n(B) − n(A ∩ B) = 30 − 24 = 6
  4. 4n(neither A nor B) = n(E) − n(A ∪ B) = 80 − 68 = 12

AnswerA only 38, A ∩ B 24, B only 6, outside 12

Part (bi) · 1 mark

Probability of being in both A and B.

  1. 1Number in A ∩ B is 24
  2. 2Total in E is 80
  3. 3P(element in A ∩ B) = 24 / 80

Answer24/80

Part (bii) · 2 marks

Probability of being in A or not in B.

  1. 1A ∪ Bʹ means all elements in A or not in B
  2. 2This includes: in A only, in both A and B, and in neither
  3. 3So total = n(A only) + n(A ∩ B) + n(neither) = 38 + 24 + 12 = 74
  4. 4Alternatively: total = n(E) − n(B only) = 80 − 6 = 74
  5. 5P(element in A ∪ Bʹ) = 74 / 80

Answer74/80

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