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Math Help - Conditional Probability problem or not?

  1. #1
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    Conditional Probability problem or not?

    If a person with weapon walks thru the security check point, the probability of the check point correctly alarmed is .92. If a person without weapon walks thru, the check point falsely alarmed its danger with the probability of .08. Suppose that the probability of a person with weapons show up is 0.05.

    Find the probability that a person has weapon if the checkpoint was not alarmed.

    My solution so far:

    I let W= \{ person \ with \  weapon \  present \} , and  A = \{ Check \ point \ is \ alarmed \}

    So I'm looking for P ( W \mid A^c ) = \frac { P(W \cap A^c ) }{ P(A^c)}

    But how do I find P(A^c)? Thank you.
    or by the Baye's Theorem, I know that  P ( W \mid A^c ) = \frac {P(A^c)}{ P(W) }P(A^c \mid W)
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  2. #2
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    Well you know several things.
    P(A|W)=.92,~P(A^c|W)=0.08,~P(W)=0.05,~P(A|W^c)=0.0  8
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