Edexcel A Level Maths: Statistics:復(fù)習(xí)筆記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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