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

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

But how do I find $\displaystyle P(A^c)$? Thank you.

or by the Baye's Theorem, I know that $\displaystyle P ( W \mid A^c ) = \frac {P(A^c)}{ P(W) }P(A^c \mid W) $