Venn Diagrams with Conditional Probability (Cambridge (CIE) AS Maths): Revision Note

Exam code: 9709

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Paul

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Further Venn Diagrams

What do you mean by further Venn diagrams?

  • The Venn diagrams used here are no more complicated than those in the first Venn Diagrams revision note, however

    • questions may use set notation as well, or alongside contextual questions

    • there may be more detailed use of conditional probability

    • mutually exclusive, three events and other unusual Venn diagram setups may be involved

2-3-3-cie-fig0-special-venn

How do I solve conditional probability problems using Venn diagrams?

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

  • 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 " single space shading " end fraction

plx9zFR~_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.

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

2-3-3-ciie-fig2-we-solution_part1
2-3-3-ciie-fig2-we-solution_part2

Examiner Tips and Tricks

  • Although very versatile, Venn diagrams may not always be the best option

    • use a tree diagram if one event follows another

e.g.  two beads drawn from a bag without replacement

  • use a two-way table for showing how many items/people are in associated categories
    e.g.  A school year group split by gender selecting which sport they wish to play

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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.

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