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
- questions may use set notation as well, or alongside contextual questions (union), (intersection) , ‘ (complement), | ("given that")
- more detailed use of conditional probability
- three events for each experiment and three experiments could be used
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 P(B | A) would be the branch for event B 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!
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 .
- Be wary of assuming that “given that” statements will always be referring to something on the second set of branches (2nd experiment), they can work the other way!