In significant effor to help prevent a terrorist attack, administrators at a major airport install many video cameras and fingerprint scanners, so thst each would-be flyers has his/her image caught on camera (and processed by facial recognition software) and his/her fingerprint scanned (and processed by fingerprint identification software).
Suppose that each procedure has a 1% false-positive rate and a 1% false-negative rate (independent of the other procedure).
Suppose 0.001% of the would-be flyers at the airport are terrorists. A given person attempting to board a plane is flagged as a potential terrorist by this procedure. What is the probability that the person is a terrorist? If insufficient information is given to solve the problem, indicate what information would be needed, provide it, and then solve the problem.
(Hint: you will need to make use of independence to solve this problem; if a person is a terrorist, there is a 99% chance that he/she will be identified as such by the facial recognition software and independent of that there is a 99% chance that he/she will be identified as a terrorist by thr fingerprint analysis software.)