Lemmara logoLemmaraWorked solution

4MA1/1F Jun 2018, Question 17: Probability with Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using a Venn diagram with numbers placed in regions of sets A, B and C, find listed set memberships, judge a statement about A ∩ C, and find a probability for C′.

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

Part (ai) · 1 mark

List the numbers that belong to set A.

  1. 1Identify all numbers inside circle A: 1, 2, 3, 4, 6, 12

Answer1, 2, 3, 4, 6, 12

Part (aii) · 1 mark

List the numbers in the union of B and C.

  1. 1B ∪ C means every number that is in B, in C, or in both
  2. 2From the diagram, B contains 1, 3, 5, 7, 9 and 11
  3. 3C contains 5 and 10
  4. 4Putting them together: 1, 3, 5, 7, 9, 10, 11

Answer1, 3, 5, 7, 9, 10, 11

Part (b) · 1 mark

Decide whether A ∩ C = ∅ is correct and give a reason.

  1. 1No number appears in both circle A and circle C
  2. 2So A ∩ C has no members
  3. 3Yes, because no number is in both A and C, so the sets do not overlap

AnswerYes, because no number is in both A and C, so the sets do not overlap

Part (c) · 2 marks

Find the probability a randomly picked number lies in C′.

  1. 1There are 12 numbers in the Venn diagram altogether
  2. 2Set C contains 5 and 10, so 2 numbers are in C
  3. 3C′ is everything not in C, so that is 12 − 2 = 10 numbers
  4. 4P(C′) = 10/12 (= 5/6)

Answer10/12

Stuck on a step? Read the free lesson: Probability with Venn Diagrams

Practise more probability with 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 probability with venn diagrams

Also searched as: 4MA1 1F June 2018 · 4MA1/1F · 4ma1 jun18 1f · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.