Question

In: Statistics and Probability

A biometric security device using fingerprints refuses to admit 1 in 100 of the authorized persons....

A biometric security device using fingerprints refuses to admit 1 in 100 of the authorized persons. Assume that 90% of those individuals who seek access are authorized.

a. If the alarm goes off and a person is refused admission, what is the probability the person was really authorized?

b. What is the probability that a person seeking to enter the facility will either be unauthorized or will not be admitted?

c. If building security conducts random personnel checks inside the building, what is the probability that a randomly selected person will be properly authorized?

d. Explain whether admittance to the building and lack of authorization to enter the facility are mutually exclusive events.

e. There are a total of 12 guards working at this facility, and on an given day, 4 will work during the day on one of four shifts. How many different possible daily job schedules are there if the order of the shifts matter?

Expert Solution

There are two different events, admittance to the event and authorization. The accuracy of biometric security is 99%.

We have the following conditional distribution table

	Admitted	Refused access	Total
Authorized	99% of 0.9 =0.891	1% of 0.9 = 0.009	0.9(90%)
Unauthorized	1% of 0.1 = 0.001	99% of 0.1 =0.099	0.1
Total	0.892	0.108	1

a) The probability that a person is refused admission given that he was authorized

b) The probability that a person seeking to enter the facility will either be unauthorized or will not be admitted

c) The probability that a randomly selected person will be properly authorized inside the building

d) Admittance to the building and lack of authorization are not mutually exclusive events. If a person is unauthorized, there are chances that he will be admitted to the building and there are chances that he will not be admitted to the building too. Hence, both can happen together, that is, a person can be both unauthorized and get admitted to the building, though with a very tiny probability, both events can happen together, and hence they are not mutually exclusive.

e) Number of ways in which 4 guards can be selected from the 12 guards for a given day

Number of ways in which the selected 4 guards can be permuted among themselves for the 4 shifts in a day

Hence, total number of possible daily job schedules for the guards

Thank You!! Please Upvote!!

orchestra answered 1 year ago

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