Question

A blood test to detect prostate cancer in men gives a positive result 96% of the time if a person has prostate cancer, and it is 97% accurate for people who do not have the disease. What is the probability of getting a false positive result (that is, a person tests positive but does not actually have the ailment)?

Answer 1

What an interesting problem!! Also very informative if accurate. Thanks for posting.

What is the meaning of 100% - 96% = 4%?
It means that 4% of the time it does not give a positive result when it should have. This is not the answer you seek. It means that you are cancer free. Not what you want to hear if you do have it. Both these small %s are deadly. The advantage of early detection is lost.

What is the meaning of 100% - 97% = 3%?
It means that you do have the disease, but the test is reporting that you don't..

This is the test result that men should fear. Likely if it happens, a male would simply walk out of the doctor's office, breathing easily because he would give anything to have this be the correct results. In the meantime, the cancer cells are spreading.

Answer 2

3%

Explanation:

Given that a blood test to detect prostate cancer in men gives a positive result 96% of the time if a person has prostate cancer, and it is 97% accurate for people who do not have the disease.

The probability of getting a false positive result (that is, a person tests positive but does not actually have the ailment)

= Prob that a person does not have the disease but test declared positive

= Prob of not accurate report for people who donot have the disease

=1-0.97

=0.03

Or 3% is the answer.