Edexcel A Level Maths: Statistics:复习笔记3.2.2 Further Venn Diagrams

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

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

 

Exam Tip

  • 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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