The Problem: There is a new test that will test for the HIV virus, but we are not sure of whether this test's results are usually correct or not. We are given the following information:
$ P (+ | HIV) = 0.9, P (- | HIV) = 0.1\! $
$ P (+ | no HIV) = 0.1, P (- | no HIV) = 0.9\! $
We are also given that only $ 0.5%\! $ have the HIV virus. The rest do not.
Are the results usually correct, and what can you tell from the results?
The Solution:
