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.

- If we are able to improve the accuracy, the false-negative rate was reduced to 10%, and the false-positive rate was reduced to 3%. And the population infection rate remains at 10 in 1000 people. Under this scenario, if a person is tested positive what is the probability that the person is really infected by the virus?