Question: A biometric security device using fingerprints erroneously refuses to admit 3 in 2 , 0 0 0 authorized persons from a facility containing classified information.

A biometric security device using fingerprints erroneously refuses to admit 3 in 2,000 authorized persons from a facility containing classified information. The device will erroneously admit 3 in 1,017,000 unauthorized persons. Assume that 98 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?

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