Acertain virus infects one in every 400 people. a test used to detect the virus in a person is positive 80% of the time if the person has the virus and 8% of the time if the person does not have the virus.

A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% 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".