Venn Diagrams with Conditional Probability (Cambridge (CIE) A Level Maths): Revision Note
Exam code: 9709
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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 
 

How do I solve conditional probability problems using Venn diagrams?
- Interpreting questions in terms of AND ( - ), OR ( - ), 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  shade B  first, then shade 
the answer will then be 

Worked Example
Three events,  and 
 are such that
        events  and 
 are mutually exclusive
        
Find
(i) 
(ii) 
(iii) 


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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