n = normal
s = sick
+ = test positive
- = test negative
Pr(n+) = .1 * .99 = .099
Pr(n-) = .90 * .99 = .891
Pr(s+) = .95 * .01 = .0095
Pr(s-) = .05 * .01 = .0005
Pr(s|+) = .0095/(.099+.0095) = .08756 (=8.756%)
I am trying to revise for a test, and am working through some prep questions. I am struggling on this one, could anyone help?
Suppose there is a medical diagnostic test for a disease. The sensitivity of the
test is .95. This means that if a person has the disease, the probability that the
test gives a positive response is .95. The specificity of the test is .90. This
means that if a person does not have the disease, the probability that the test
gives a negative response is .90, or that the false positive rate of the test is .10.
In the population, 1% of the people have the disease.
What is the probability that a person tested has the disease, given the results of the test is positive? Let
D be the event "the person has the disease" and let T be the event "the test
gives a positive result."
Any help would be much appreciated.