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A certain virus infects one in every 200 people. A test used to detect the virus...

A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80​% of the time when the person has the virus and 15​% of the time when the person does not have the virus.​ (This 15​% result is called a false positive​.) Let A be the event​ "the person is​ infected" and B be the event​ "the person tests​ positive."

​(a) Using​ Bayes' Theorem, when a person tests​ positive, determine the probability that the person is infected.

​(b) Using​ Bayes' Theorem, when a person tests​ negative, determine the probability that the person is not infected.

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