There are two test for a disease: one is rapid and the other is slow. Given an infected individual, the rapid test will register positive 40% of the time, while the slow test will register positive 80% of the time: additionally, both tests will be positive 35% of the time.
- Given an infected person and that the rapid test measures a positive result, what is the probability that the slow test is also positive?
I assumed the tests were independent, giving just 80%. This is incorrect however.
I tried also P(slow) * P(rapid) = 0.80 * 0.40 = 0.32, which was also incorrect.
I also tried P(A|B) = P(A and B)/ P(B) leaving just P(A) = 0.8
I'm not sure how to incorporate the latter half of the information either. Is 35% referring to positive for all tests (infected or uninfected individuals), i.e. false-positive rate?
- Given an infected person and that the rapid test measures a negative result, what is the chance that the slow test is positive.
Same problem here. Why would the results of a rapid test affect the results of a slow test–shouldn't it just be 80%?
Best Answer
My reading is that for an infected person
So the answers are: