2 6 points In a significant effort to help prevent a terrori

2. (6 points) In a significant effort to help prevent a terrorist attack, administrators at a major airport install many video cameras and fingerprint scanners, so that each would-be flyer 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 al% false positive rate and a 1% false negative rate (independent of the other procedure). Their system (at this hypothetical airport) works as follows: Someone is flagged as a \"potential terrorist\". and is not allowed to board the plane if and only if both procedures give a positive result (i.e., if the facial recognition software says the person is a terrorist, and if the fingerprint analysis software also says the person is a terrorist); otherwise, the person is allowed to board as usual. Suppose 0.001% of the would-be flyers at that attempting to board a plane is flagged as a potential terrorist by this procedure. What is the probability that that person is a terrorist? If insufficient information is given to solve airport are terrorists. A given person

Solution

Because there is independence between both procedures, the probability that a person flagged as a terrorist by the procedures is:

0.99x0.99=0.9801

ANSWER: 98.01%