A biometric security device using fingerprints erroneously refuse to admit 1 in 1,000 authorized person from a facility containi
ng 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?
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.
Yes they are the same. The number on the right just has an extra zero. You can add an infinite amount of zeros to the end of a number without changing it's value.