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A certain virus infects one in every 250 people. A test used to detect the virus in a person is positive 90​% of the time when the person has the virus and 10​% of the time when the person does not have the virus.​ (This
10​% 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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