# 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

#### 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