1. A biometric security device using fingerprints erroneously refuses to admit 2 in 1,800 authorized persons from a facility containing classified information. The device will erroneously admit 2 in 1,007,000 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? (Round your answer to 5 decimal places.)

Probability = ?

2.A poker hand (5 cards) is drawn from an ordinary deck of 52 cards. Find the probability of each event, showing your reasoning carefully.

a. The first four cards are the four aces. Probability = ?

b. Any four cards are the four aces. Probability = ?