Bayes' Theorem (DP IB Analysis & Approaches (AA)): Revision Note

Bayes' theorem

What is Bayes’ theorem?

• Bayes’ theorem allows you switch the order of conditional probabilities

  • If you know ,  and then Bayes’ theorem allows you to find 

• Essentially if you have a tree diagram you will already know the conditional probabilities of the second branches

  • Bayes’ theorem allows you to find the conditional probabilities if you switch the order of the events

• For any two events A and B Bayes’ theorem states:

   
  
   

  • This is given in the exam formula booklet

  • This formula is derived using the formulae:

    •  

    •  

    • and 

• Bayes’ theorem can be extended to mutually exclusive events B₁, B₂, ..., B_n and any other event A

  • In your exam you will have a maximum of three mutually exclusive events

    
    
    

    • This is given in the exam formula booklet

How do I calculate conditional probabilities using Bayes’ theorem?

• Start by drawing a tree diagram

  • Label B₁ & B₂ (& B₃ if necessary) on the first set of branches

  • Label A & A’ on the second set of branches

• The questions will give you enough information to label the probabilities on this tree

• Identify the probabilities needed to use Bayes’ theorem

  • The probabilities will come in pairs: and