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First teaching 2021

Last exams 2024

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Probability & Venn Diagrams (CIE IGCSE Maths: Core)

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Paul

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Probability & Venn Diagrams

What is a Venn diagram?

  • Venn diagrams allow us to show two characteristics of a situation where there is overlap between the characteristics
  • For example, students in a sixth form can study biology or chemistry but there may be students who study both

What might I be asked to do with a Venn diagram?

  • You can be asked to
    • draw a Venn diagram and/or
    • interpret a Venn diagram
  • Strictly speaking the rectangle (box) is always essential on a Venn diagram
    • it represents everything that can happen in the situation
    • you may see the letter calligraphic E or xi written inside or just outside the box
      • this means “the set of all possible outcomes” - i.e. “everything”!
      • sometimes the letters U or S are used instead
  • The words AND and OR become very important in both drawing and interpreting Venn diagrams
  • You will need to be familiar with the symbols ∩ and ∪
    • ∩ is intersection
    • ∪ is union
    • these mean AND and OR (respectively)

How do I draw a Venn diagram?

  • Start with a “box” and overlapping “bubbles”
    • there will be two bubbles
  • Work through each sentence/piece of information given in a question to begin completing sections of your Venn diagram
    • pieces of information may have to be combined before you can enter a value into the diagram
    • not all values will be given directly
      • some may need working out
      • you will be expected to do this to complete your Venn diagram
  • Remember to consider AND and OR

How do I interpret a Venn diagram?

  • Use the information in the question to identify the parts of the Venn diagram needed to answer it
  • Shading the relevant parts of a Venn diagram can be helpful
  • Be careful with probability notation such as
    • the symbols ∩ and ∪
      • A∩B is just the middle of the two bubbles
      • A∪B is anything that is in at least one of the bubbles

Examiner Tip

  • You may have to use your Venn diagram more than once in a question
    • so shading the original diagram can become confusing if you're trying to use it more than once
    • draw a 'mini'-Venn diagram (a small quick sketch just showing the box and bubbles but no values) and shade that

Worked example

In a class of 30 students, 15 students study Spanish, and 3 of the Spanish students also study German.
7 students study neither Spanish nor German.

a)

Draw a Venn diagram to show this information.

We start with the 3 in the intersection ("overlap"); we can then deduce the "Spanish only" section is 12.
7 needs to be outside both bubbles but within the box.
With a total of 30 we can work out how many students study "German only" and complete the diagram.

b)

Use your Venn diagram to find the probability that a student, selected at random from the class, studies Spanish but not German.

Highlight the part "Spanish only".

Venn-Q1b-Working, downloadable IGCSE & GCSE Maths revision notes

Pick out the numbers you need carefully.

Students studying "Spanish only" = 12
Total number of students = 30

P(Spanish only) bold equals bold 12 over bold 30 stretchy left parenthesis equals 2 over 5 stretchy right parenthesis 

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.