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

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!

Worked Example

The event  has a 75% probability of occurring.

The event follows event , and if event has occurred, event  has an 80% chance of occurring.

It is also known that  .

Find

(i)
(ii)
(iii)the probability that event didn’t occur, given that event didn’t occur.

 

 

Exam Tip

  • It can be tricky to get a tree diagram looking neat and clear first attempt – it can be worth drawing a rough one first, especially if there are more than two outcomes or more than two events; do keep an eye on the exam clock though!
  • Always worth another mention – tree diagrams make particularly frequent use of the result
  • Tree diagrams have built-in checks
    • the probabilities for each pair of branches should add up to 1
    • the probabilities for each outcome of combined events should add up to 1

转载自savemyexams

更多Alevel课程
翰林国际教育资讯二维码