IB DP Maths: AA HL復習筆記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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