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Bayes' theorem

  1. Jun 20, 2017 #1
    1. The problem statement, all variables and given/known data

    A crime has been committed and the police have only captured a suspect, although he obviously claims to be innocent. To give a verdict the judge authorizes the use of the lie detector. The manufacturer of the device warns the authority that the lie detector in 10% of the cases in which it has been used showed a positive reading (that is to say lie), since in fact the suspect spoke with the truth. So too, the detector in 95% of the cases, has given a positive reading when the suspects really lied.
    A) tell a lie the detector shows a positive reading
    B) do not tell a lie and the detector shows positive reading
    C) tell a lie and the detector shows negative reading
    D) do not lie and the detector shows a negative reading

    2. Relevant equations


    3. The attempt at a solution
    well this might be too simple or to complex i dont know, but i need to know if i am right in my responses because my career is in play.
    a)95%
    b)10%
    c)5%
    d)90%
    i use the complement of probabilities to estimate the ungiven probabilities if i am wrong please help me
    pr(F/T)=0.10 pr(Fc/T)=0.90
    pr(F/L)=0.05 pr(Fc/L)=0.95
     
  2. jcsd
  3. Jun 20, 2017 #2

    mfb

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    Is that the exact problem statement in English? It has a strange phrasing.
     
  4. Jun 20, 2017 #3
    Yes it is, in fact very weird problem
     
  5. Jun 20, 2017 #4

    mfb

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    (A) to (D) are not even complete sentences, and there is no actual problem statement.

    I guess your interpretation is reasonable, but it is really guesswork. With the given numbers you cannot calculate more than what you did.
     
  6. Jun 20, 2017 #5

    haruspex

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    Because it is a translation it is hard to be sure, but in English the questions read as though they refer to joint probabilities (lie AND positive). That would require some a priori probability of a lie, which we do not have, but if we were to have such the whole question setting would make more sense. It would lead into asking the probability of guilt given the result of the lie detector. Very Bayesian.
     
  7. Jun 21, 2017 #6
    i can swear that the problem is like that, i think the problems are designed by the profesor, cant find it in the internet, so its very weird
    just gives two data as you can see above and 4 questions i cant put the questions in this way
    a) probability of lie given the detector shows positive reading i think this mean pr(L/Fc)
     
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