A biometric security device using fingerprints erroneously refuse to admit 1 in 1,000 authorized person from a facility containing classified information. The device will erroneously admit 1 in 1,000,000 unauthorized persons. Assume that 95 percent of those who seek access are authorized. If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized?

0.01864

Step-by-step explanation:

Let A be the event that a person was authorized and NA be the event that the person was not authorized. Let R be the event that a person was refused admission and G be the event that a person was granted admission.

Then we have to find P (A|R) = [P (A) * P (R|A) ]/P (R)

putting value we get

P (R) = P (A) P (R|A) + P (NA) P (R|NA) = 0.95 * (1/1000) + 0.05 * ((1,000,000-1) / 1,000,000) = 0.0.05094995

P (A|R) = [P (A) * P (R|A) ]/P (R)

= [0.95 * (1/1000) ] / (0.05094995)

=0.01864