Question

A certain disease has an incidence rate of 0.2%. If the false negative rate is 6% and the false positive rate is 3%, compute the probability that a person who tests positive actually has the disease.

Answer 1

The incidense rate of the disease is 0.002

The false negative rate is 0.06

And the false positive rate is 0.03

For every 100000 people, 200 would have the disease

Between thes, a total of 0.06*200 = 12 will test negative

Then, the remaining 188 will test positive

Between the 99800 who are healthy, a total of 0.03*99800 = 2994 will test positive.

Then, a total of 2994 + 188 = 3182 will test positive, and the probability that a person who tests positive will have the disease is 188/3182 = 0.059 = 5.9%