A certain virus infects 10 in every 1000 people.

A test used to detect the virus is accurate 80% of the time when the person has the virus (20% false negative). The test is accurate 95% of the time when the person does not have the virus (5% false positive).

That is 20% of the time when the test should return positive but didn't, and 5% of the time the test returned positive but shouldn't.

1) Out of all people who tested positive, what portion is really infected? In another word, if a person is tested positive, what is the probability that the person is truly infected by the virus? ANSWER: AROUND 13%.

Please help.