A LevelMathsCambridge (CIE)Probability & Statistics 1Revision NotesProbabilityBasic ProbabilityVenn Diagrams

Venn Diagrams (Cambridge (CIE) A Level Maths) : Revision Note

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Venn Diagrams

What is a Venn diagram?

  • A Venn diagram is a way to illustrate events and are particularly useful when outcomes overlap

  • Venn diagrams are mostly used for 2 or 3 events

  • A Venn diagram consists of a box (rectangle) and a bubble (circle/ellipse) for each event

    • Bubbles may or may not overlap

    • Bubble(s) is not a technical term, but we like it!

  • The box represents all outcomes

    • It is often referred to as the Universal Set and is commonly labelled with the symbols calligraphic E (Kunstler script font uppercase letter E)size 16px S size 16px comma size 16px space size 16px U size 16px space size 16px or size 16px space size 16px xi  (Greek lowercase letter Xi)

    • There is no standardised symbol for this purpose

  • Bubbles are labelled with their event name (A, B, etc)

  • The numbers inside a Venn diagram (there should be one in each region) will represent either a frequency or a probability

    • In the case of probabilities being shown, all values should total 1

2-1-2-cie-fig1-basic-venns

What do the different regions and bubbles overlapping mean on a Venn diagram?

  • This will depend on how many events there are and how the outcomes overlap

  • Venn diagrams show ‘AND’ and ‘OR’ statements easily

2-1-2-cie-fig2-various-venns

Worked Example

40 people were surveyed regarding which games consoles they owned.

8 people said they owned a Playstation 5 (P) and an Xbox Series X (X).

5 people said they owned neither of these consoles.

Of those people that owned only one games console, twice as many owned an Xbox Series X as a Playstation 5.

One of the 40 people is chosen at random.  Find the probability that this person 

(i) owns both consoles,

(ii) owns exactly one console,

(iii) doesn’t own a Playstation 5.

2-1-2-cie-fig3-we-solution

Examiner Tips and Tricks

  • The rectangle in a Venn diagram is a key part of the diagram

    • it represents all possible outcomes of the experiment

    • the bubbles merely represent the events we are particularly interested in

    • there is usually a few possibilities that fall outside of these events so this would be the section outside the bubbles but inside the rectangle

  • A quick ‘mini-Venn’ diagram shading the parts required to answer the question can be useful rather than always drawing a full Venn diagram with all its values

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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

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.

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