A certain virus infects one in every 250 people. A test used to detect the virus...

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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 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. i Click the icon to the right to review Bayes' Theorem. (a) The probability that a person is infected when a person tests positive is (Do not round until final answer. Then round to three decimal places as needed.) (b) The probability that a person is not infected when a person tests negative is. (Round to four decimal places as needed.) A certain virus infects one in every 250 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. i Click the icon to the right to review Bayes' Theorem. (a) The probability that a person is infected when a person tests positive is (Do not round until final answer. Then round to three decimal places as needed.) (b) The probability that a person is not infected when a person tests negative is. (Round to four decimal places as needed.)