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
- The wording/terminology used in questions and on diagrams may now involve the use of set notation including the symbols ∪(union), ∩(intersection) and ‘ (complement)
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
- e.g. If given, possibly in words,
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!
- from Conditional Probability,
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.
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
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