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Bayes Theorem Question - Am I doing this right?

  1. Sep 20, 2009 #1
    Another Conditional Problem...

    Lie Detector is
    95% reliable when the person is guilty
    98% reliable when innocent

    Random Person pulled from a pool of people... This pool is 6% guilty of theft and 94% have never stolen...

    Random person was determined guilty from the lie detector, what is the probability he is innocent?

    My attempt...

    (.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7512 . so 75.12% chance of him being guilty. Seems low, but I guess the fact that the pool of people has only 6% guilty in it, it lowers the chance a lot.
  2. jcsd
  3. Sep 20, 2009 #2


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    Homework Helper

    I get
    (.95)(.06) / [(.95)(.06) + (.02)(1-.06)] = .7520
    This is a famous paradox
    If a test is fairly accurate, but the population mostly negative a positive test is not very reliable.
  4. Sep 20, 2009 #3
    Pretty crazy, but thanks for the help :)
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