I have the following question where I have to calculate the posterior probabilty of a person having a certain disease.
P(patient has disease|heterosexual, non drug user) = 0.00001
P(Test pos. | disease) = 0.9
P(Test pos. | no disease) = 0.2
to write it in an easier way:
P(D) = 0.0001
P(pos|D) = 0.9
P(pos|no D) = 0.2
P(no D) = 1 - P(D) ???
I used bayes theorem as follows:
posterior = (P(pos|D) * P(D))/(P(pos|D)*P(D) + P(pos|no D) * P(no D))
and i get as a result: 0.0045%.
Did I interpret the question right?
thanks in advance.