A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 80?% 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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