I am trying to translate the following question into input for the Bayes' theorem.
What i have currently is P(V|A) = 0.95 which is the probability of having the virus given that test A recognises it which is 95%, and P(V|~A) = 0.10 which is the prob of having the virus given that the test doesn't detect it, Also P(V) = 0.01 because 1% of people have the virus.
I am wondering if i have misinterpreted the "Test A" part of the question?
Consider two tests, A and B, for a virus.
Test A is 95% effective at recognizing the virus when it is present (that is 95% of the time that the virus is
present, the test detects it), but has a 10% false positive rate (that is, 10% of the time it indicates the virus
is present when it is not).
Test B is 90% effective at recognizing the virus, but has a 5% false positive rate.
The two test use different, independent, methods of indentifying the virus.
1% of all people have the virus.
Joe tests positive for the virus using test A. Bob tests positive using test B. Who is more likely to have the
virus?
Best Answer
The false positive rate is $P(A\mid\sim V)$ (probability the test erroneously comes back positive when you don't have the virus) and the effectiveness is $P(A\mid V)$ (probability the test correctly comes back positive when the virus is present). You use these, $P(V)$ (which you identified correctly) and bayes to figure out $P(V\mid A)$, the probability a person actually has the virus if they tested positive.