A certain virus infects 1 of every 200 people. A test used to detect the virus on a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. (This 5% result is called a false positive) Let A be the event "the person is infected" and B be the event " the person tests positive."


Find the following probabilities correctly to 4 decimal places.


Use Bayes Theorem to find the probability that a person is indeed infected given that the test is positive.

Use Bayes Theorem to find the probability that a person is NOT infected given that the test is negative.