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IB DP Maths: AA HL復習筆記4.3.3 Bayes' Theorem

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月13日 上午10:52

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.

4-3-3-ib-aa-hl-bayes-theorem-a-we-solution

b)? ? ? ?Given that Lucy answered a question correctly, find the probability that it was about TV.

4-3-3-ib-aa-hl-bayes-theorem-b-we-solution

 

 

 

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