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Conditional probability and Bayes' theorem

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Useful for: IB Math AA HL AP® Statistics

Learn it P(A | B) = P(A and B) ÷ P(B). Bayes' theorem reverses a condition: P(A | B) = P(B | A)P(A) ÷ P(B). Tree diagrams make this clear. Medical tests are the classic example.

Example: 1% have a disease. A test is 95% accurate both ways. P(disease | positive)?

  1. P(positive) = 0.01(0.95) + 0.99(0.05) = 0.059.
  2. P = 0.0095 ÷ 0.059 ≈ 0.161: only about 16%!

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