A test has a true positive rate of 100% and a false-positive rate of 5%. There is a population with a 1/1000 rate of having the condition the test identifies. Considering a positive test, what is the probability of having that condition?

Let’s suppose you are being tested for a disease if you have the illness the test will end up saying you have the illness. However, if you don’t have the illness- 5% of the times the test will end up saying you have the illness and 95% of the times the test will give an accurate result that you don’t have the illness. Thus there is a 5% error in case you do not have the illness.

Out of 1000 people, 1 person who has the disease will get true positive result.

Out of the remaining 999 people, 5% will also get true positive result.

Close to 50 people will get a true positive result for the disease.

This means that out of 1000 people, 51 people will be tested positive for the disease even though only one person has the illness. There is only a 2% probability of you having the disease even if your reports say that you have the disease.