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

Tree diagrams with conditional probability

How do I find conditional probabilities problems from tree diagrams?

• Interpreting questions in terms of AND (), OR () and complement ( ‘ )

• Condition probability may now be involved too - “given that” ( | )

• 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  would be the branch for event  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 the next revision note

• (“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!