Question: Problem 4 Consider a rare virus and its screening test data performed on a certain population. The events C and NC denote that a person

Problem 4 Consider a rare virus and its screening test data

Problem 4 Consider a rare virus and its screening test data performed on a certain population. The events C and NC denote that a person is either a carrier or a non-carrier of this virus, respectively. Also, the events 'Pos' and 'Neg' denote that a person (who has been tested) shows positive and negative test results, reSpectively. It is known that 0.5% of the population tested is a carrier. It is also known that the screening test procedure is not perfect. There is a 0.5% chance to obtain a positive test result from a non-carrier and a 5% chance to obtain a negative test result from a person that is in reality a carrier. Compute the following: (a) The probability that a person tested is a non-carrier given that the test result is positive. (b) The probability that a person tested is a non-carrier given that the test result is negative. (0) The probability that a person tested is a carrier given that the test result is positive. (d) The probability that a person tested is a carrier given that the test result is negative. (e) The probability that a person tested is a non-carrier and that the test result is positive. (f) The probability that a person tested is a carrier and that the test is negative

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