Question

A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person has the virus and 5% of the time if the person does not have the virus. Using Bayes' Rule, if a person tests positive, determine the probability the person has the virus. Round to four decimal places.

Answer 1

P(Virus) = 1/200 = 0.005

So P(No Virus) = 1 - 0.005 = 0.995

P(Positive | Virus) = 0.80

P(Positive | No Virus) = 0.05

Hence by Baye's theorem:

P(Virus | Positive)

$= \frac{0.005*0.80}{0.005*0.80+0.995*0.05}$

= 0.0744 [Rounded off to 4 decimal places]