Lemmara logoLemmaraWorked solution

4MA1/2HR Jan 2019, Question 16: Three-Set Venn Diagrams

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

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

From survey data on 120 visitors and their use of swimming, basketball and gym, fill a three-set Venn diagram and find a conditional probability for a swimmer.

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

Part (a) · 3 marks

Use the given counts, including overlaps, to work out the number in every region of the three-circle Venn diagram.

  1. 1Centre (all three) = 2
  2. 2Two only: S and B 3 − 2 = 1, B and G 5 − 2 = 3, S and G 7 − 2 = 5
  3. 3One only: S 28 − 8 = 20, B 16 − 6 = 10, G 27 − 10 = 17
  4. 4Inside the circles there are 58, so outside = 120 − 58 = 62
  5. 5S, B and G all: 2; S and B only: 1; B and G only: 3; S and G only: 5; S only: 20; B only: 10; G only: 17; outside all three circles: 62

AnswerS, B and G all: 2; S and B only: 1; B and G only: 3; S and G only: 5; S only: 20; B only: 10; G only: 17; outside all three circles: 62

Part (b) · 1 mark

Given a person went swimming, find the probability they also played basketball.

  1. 1The person is chosen from the 28 people who went swimming
  2. 2Of those, the ones who also played basketball are 1 + 2 = 3
  3. 3Probability = 3/28

Answer3/28

Stuck on a step? Read the free lesson: Three-Set Venn Diagrams

Practise more three-set venn diagrams questions

Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on three-set venn diagrams

Also searched as: 4MA1 2HR January 2019 · 4MA1/2HR · 4ma1 jan19 2hr · question 16.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.