A LevelMathsAQAStatisticsRevision NotesProbabilityFurther ProbabilityVenn Diagrams with Conditional Probability

Venn Diagrams with Conditional Probability (AQA A Level Maths): Revision Note

Exam code: 7357

Paul

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Paul

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AQA Maths: StatisticsOCR Maths A: StatisticsEdexcel Maths: Statistics

Venn diagrams with conditional probability

How do I find conditional probabilities from a Venn diagram?

  • Interpreting questions in terms of OR (union), AND (intersection), complement ( ‘ ) and “given that” ( | )

  • Conditional probability may now be involved too

  • Use mini-Venn diagrams to sketch and shade the regions you are dealing with – use different colours if available or different styles of shading if not

    • Shading can help you see the answer

  • since straight P left parenthesis A vertical line B right parenthesis equals fraction numerator straight P left parenthesis A italic intersection B right parenthesis over denominator straight P left parenthesis B right parenthesis end fraction shade B first, then shade A intersection B

    • the answer will then be fraction numerator " double space shading " over denominator " all space shading " end fraction

3-2-2-fig1-set-notation-examples

Worked Example

Three events, A comma space B and C are such that

        events A and C are mutually exclusive

        straight P left parenthesis A intersection B right parenthesis equals 0.2 straight P left parenthesis B intersection C right parenthesis equals 0.3 straight P left parenthesis left parenthesis A union B union C right parenthesis apostrophe right parenthesis equals 0.1 straight P left parenthesis B right parenthesis equals 0.7 straight P left parenthesis A apostrophe right parenthesis equals 0.75.

(a) Draw a complete Venn diagram to show the probabilities connecting the three events.

 (b) Find 

(i) straight P left parenthesis A vertical line B right parenthesis

(ii) straight P left parenthesis A apostrophe vertical line C apostrophe right parenthesis

(iii) straight P left parenthesis C vertical line left parenthesis A union B right parenthesis apostrophe right parenthesis

3-2-2-fig2-we-solution-part-1
3-2-2-fig2-we-solution-part-2-luggage-removed

Examiner Tips and Tricks

  • Always draw the box in a Venn diagram; it represents all possible outcomes of the experiment so is a crucial part of the diagram, the bubbles merely represent the events we are particularly interested in

  • You may be able to answer some questions by applying formulae or you may prefer to use shaded mini-Venn diagrams; complicated questions tend to be easier with mini-Venn diagrams

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    Paul

    Author: Paul

    Expertise: Maths Content Creator

    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.