# 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,
• 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