A biometric security device using fingerprints refuses to admit 1 in 50 persons from a facility containing classified information.

A biometric security device using fingerprints refuses to admit 1 in 50 persons from a facility containing classified information. The device will erroneously refuse to admit 1 in 100 of the authorized persons. Assume that 90% of those individuals who seek access are authorized.
1.If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized? 
2.What is the probability that a person seeking to enter the facility will either be unauthorized or will not be admitted?
3.If building security conducts random personnel checks inside the building, what is the probability that a randomly selected person will be properly authorized? 
4.Explain whether admittance to the building and lack of authorization to enter the facility are mutually exclusive events.
5.There are a total of 12 guards working at this facility, and on any given day, 4 will work at during the day on one of four shifts. How many different possible daily job schedules are there if the order of shifts matter?
 
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