Airport screening is designed to detect most things that can be used as a weapon, primarily firearms.  If the screening “beeps” (meaning it has detected something), it is right 90% of the time.  That is, if there is something illegal present, it will detect this with probability 0.9.  It can also “beep” when there is nothing illegal present; this happens 15% of the time.  Empirical evidence shows that 2% of the people going through airport screening have something with them that is illegal.   a. If the screening machine “beeps,” what is the probability the person has something illegal with them?   b. What percentage of the people going through screening get “beeped?”   c. Note that the 0.90 probability of detecting something and the 0.15 probability of falsely detecting something don’t add to 1.0. Is that a problem?  If not, why not

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