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.

Question

09-06-2024
Mathematics

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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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