IB DP Maths: AA HL复习笔记4.3.3 Bayes' Theorem
Bayes' Theorem
What is Bayes’ Theorem
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
Exam Tip
- In an exam you are less likely to make a mistake when using the formula if you draw a tree diagram first
Worked Example
Lucy is doing a quiz. For each question there’s a 45% chance that it is about music, 30% chance that it is about TV and 25% chance that it is about literature. The probability that Lucy answers a question correctly is 0.6 for music, 0.95 for TV and 0.4 for literature.
a) Draw a tree diagram to represent this information.
b) Given that Lucy answered a question correctly, find the probability that it was about TV.
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