A certain disease occurs in 4% of the population. A blood test for this disease shows a false positive 12% of the time. That means a test will show positive given that the person does not have the disease. What is the probability that a person tests positive but does not have the disease?

Question

A certain disease occurs in 4% of the population.  A blood test for this disease shows a false positive 12% of the time.  That means a test will show positive given that the person does not have the disease.  What is the probability that a person tests positive but does not have the disease?

Note: The answer is 0.1152, but I don't know how they get it. Please help me and show the steps please. Thanks.

John · Answer

.12 times .96 false positive times % who don't have the disease.