In: Statistics and Probability
A certain virus infects one in every
150
people. A test used to detect the virus in a person is positive
80%
of the time when the person has the virus and
55%
of the time when the person does not have the virus. (This
55%
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.