Edexcel A Level Maths: Statistics:复习笔记3.2.3 Further Tree Diagrams

What do you mean by further tree diagrams?

• The tree diagrams used here are no more complicated than those in the first Tree Diagrams revision note, however
  • The wording/terminology used in questions and on diagrams may now involve the use of set notation including the symbols ∪(union), ∩(intersection) and ‘ (complement)
    • e.g.  P(A') would be used for “P(not A)”
  • Conditional probability questions can be solved using tree diagrams

How do I solve conditional probability problems using tree diagrams?

• Interpreting questions in terms of AND (∩), OR (∪), complement ( ‘ ) and “given that” ( | )
• Condition probability may now be involved too
• This makes it harder to know where to start and how to complete the probabilities on a tree diagram
  • e.g. If given, possibly in words,  then event A has already occurred so start by looking for the branch event A in the 1st experiment, and then  would be the branch for event  in the 2nd experiment

Similarly,  would require starting with event “ ” in the 1st experiment and event B in the 2nd experiment

• The diagram above gives rise to some probability formulae you will see in Probability Formulae
• (“given that”) is the probability on the branch of the 2nd experiment
• However, the “given that” statement  is more complicated and a matter of working backwards
  • from Conditional Probability,
  • from the diagram above,
  • leading to 
  • This is quite a complicated looking formula to try to remember so use the logical steps instead – and a clearly labelled tree diagram!

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