Question

A certain disease has an incidence rate of 2%. The false negative rate is 5%, and the false positive rate is 1%. Compute the probability that a person who tests positive actually has the disease. Give your answer to 2 decimal places.

Answer 1

Consider a population of 100,000 who get the test. Of those people, .2%, or 200 people actually have the disease,but 5% will test negative, so 190 out of those 200 will test positive.

=(200*5)/100 = 10;

=200-10 = 190

Of the 99,800 who don't have the disease, 1%, or 998 will test positive.

=(99800*1)/100 = 998

In total, (190+998) =1188 will test positive, of which 190 will actually have the disease. So the ratio of diseased to positive tests is 190/1188 , or 0.159933. 0.16(round to two decimal places) This is the probability that someone who tested positive actually has the disease

Answer: 0.16