Tree Diagrams with Conditional Probability (Cambridge (CIE) A Level Maths): Revision Note

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

  • 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 1^st experiment, and then P(B | A)  would be the branch for event B in the 2^nd experiment

Similarly,  would require starting with event “ ” in the 1^st experiment and event B in the 2^nd 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 2^nd 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!