Venn Diagrams with Conditional Probability (Edexcel A Level Maths): Revision Note
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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
Venn diagrams, and the wording/terminology in questions, may now involve the use of set notation including the symbols
(union),
(intersection), ‘ (complement) and | (“given that”)
Conditional probability problems can be solved using Venn diagrams
How do I solve conditional probability problems using Venn diagrams?
Interpreting questions in terms of AND (
), OR (
), 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 shade B first, then shade
the answer will then be
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Worked Example
Three events, and
are such that
events and
are mutually exclusive
(a) Draw a complete Venn diagram to show the probabilities connecting the three events.
(b) Find
(i)
(ii)
(iii)
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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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