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Bayes' theorem

  1. May 20, 2013 #1
    in the Bayes' theorem, why P(B|A)*P(A) is divided by P(B)? What we want no achieve with the fraction?
  2. jcsd
  3. May 20, 2013 #2

    D H

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    Start with the definition of conditional probability:
    [tex]P(B|A) \equiv \frac{P(A\cap B)}{P(A)}[/tex]
    and similarly,
    [tex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/tex]
    Solving for [itex]P(A\cap B)[/itex] yields
    [tex]P(A\cap B) = P(B|A)P(A) = P(A|B)P(B)[/tex]
    Bayes' theorem derives directly from this.
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