A biometric security device using fingerprints erroneously refuses to admit 1 in 1,000 authorized persons 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?

Out of x persons, 95% are authorized. 1/1000 are refused.
Out of x persons, 5% are unauthorized. 999,999/1,000,000 are refused.

So: (x*.95*1/1000)/(x*.05*999,999)=.00095/.0499995=.019
So there is a 1.9% chance that the person was really authorized.

A biometric security device using fingerprints erroneously refuses to admit 1 in 1,800 authorized persons from a facility containing classified information. The device will erroneously admit 1 in 1,018,000 unauthorized persons. Assume that 90 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?

Does anyone knows the answer to this?

What does this to do with economics?

A biometric security device using fingerprints erroneously refuses to admit 1 in 1,000 authorized persons 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?

See the post above by leifweaver.