Mathematics

Jeremy Heath

17 February, 05:03

A certain virus infects one in every 150 people. A test used to detect the virus in a person is positive 70% 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. Here is the formula that we are given for this particular problem:P (A|B) = P (A) x P (B|A) divided byP (A) x P (B|A) + P (A') x P (B|A')