Find the probability that a person has the virus given that they have tested positive.

Answer 1

P(V/P)P(P) = P(P/V)P(V)

P(V/P) = P(P/V)P(V)/P(P)

That's Bayes' Theorem

If you know the P(V), the probability of having the virus, P(P) the probability of testing positive and P(P/V) the probability of testing positive if you have the virus, then you can calculate P(V/P) the probability of having the virus if you test positive.

Let's say, for example, if 10% of the population has the virus, and you have a test that always results in positive if you have the virus, and 20% test positive then

P(V/P) = .1(1)/.2 = 1/2 = 50% chance you have the virus if you test positive. In other words with this scenario, there are no false negatives, but a lot of false positives.