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 , and

So I'm looking for

But how do I find ? Thank you.

or by the Baye's Theorem, I know that