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Math Help - posterior probability question

  1. #1
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    Unhappy posterior probability question

    hi
    in the attachment is the question
    I have problem solving it
    from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
    after he did the experiment he found that it is correct 100 %
    but I could not find where is the posterior
    Prior Probability =0.2
    correcting information= 1
    posterior =?
    until now this is what I came up with

    thank you in advance
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  2. #2
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    Quote Originally Posted by Logical View Post
    hi
    in the attachment is the question
    I have problem solving it
    from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
    after he did the experiment he found that it is correct 100 %
    but I could not find where is the posterior
    Prior Probability =0.2
    correcting information= 1
    posterior =?
    until now this is what I came up with

    thank you in advance
    Prior: Pr(T > 10) = 0.2

    Pr(Data | T > 10) = 1, Pr(Data | T < 10) = 0.

    \Pr(T > 10 \, | \, \text{Data}) = \frac{\Pr(T > 10 \cap \text{Data})}{\Pr(\text{Data})}.

    \Pr(T > 10 \cap \text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) = (1) (0.2) = 0.2.

    \Pr(\text{Data}) = \Pr(\text{Data} \, | \, T > 10) \cdot \Pr(T > 10) + \Pr(\text{Data} \, | \, T < 10) \cdot \Pr(T < 10) = (1)(0.2) + (0)(0.8) = 0.2.

    Therefore \Pr(T > 10 \, | \, \text{Data}) = \frac{0.2}{0.2} = 1.
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