A certain virus infects one in every 300

300 people. A test used to detect the virus in a person is positive 90

90% of the time when the person has the virus and 5

5% of the time when the person does not have the virus.(This 5

5% result is called a false positive.) Let A be the event"the person isinfected" and B be the event"the person testspositive."

(a) UsingBayes' Theorem, when a person testspositive, determine the probability that the person is infected.

(b) UsingBayes' Theorem, when a person testsnegative, determine the probability that the person is not infected.