Did this video help you?
Syllabus Edition
First teaching 2021
Last exams 2024
Probability & Venn Diagrams (CIE IGCSE Maths: Core)
Revision Note
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 or 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
- the symbols ∩ and ∪
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.
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.
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".
Pick out the numbers you need carefully.
Students studying "Spanish only" = 12
Total number of students = 30
P(Spanish only)
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?