A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the person is infected" and B be the event "the person tests positive."

a. Find the probability that a person has the virus given that they have tested positive; that is, find P(A|B).

b. Find the probability that a person does not have the virus given that they test negative; that is, find P(not A | not B).