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    Probability of the correct diagnosis in a lie detector

    Probability of the correct diagnosis in a lie detector
    A lie detector correctly diagnoses 90% of those who lie (M) and 95% of those who do not lie. A person is chosen at random from a group of 100 people from which 20 are known to lie. Whether that person lies or not, what is the probability that the detector will provide a correct diagnosis?

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    Re: Probability of the correct diagnosis in a lie detector

    If I understand the question correctly you need to apply the total probability formula:

    P(G)=P(G|A1)*P(A1)+P(G|A2)*P(A2) where A1 and A2 are the events that the subject lied respectively that he did not lie.

    good luck

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