Question

For a certain medical test for a disease, it has been found that the test will return a positive result 97% of the time when you the disease, but it will also retum a positive result 4\% of the time when you don't have the disease. A person takes the test. What is the probability that the will retum positive for them, if it is known that 3% of the population has the discase? You do not know if they do or don't have the disesse, so be sure to consider both cases.

Answer 1

Let P denotes that it will return the positive test.

Let D denotes that the person have disease.

The test will return a positive result 97% of the time when you the disease. So,

The test will return a positive result 4 %  the time when you don't have the disease.

3% of the population has the disease . So,

Probability that test will return positive is