What is the probability that the suspect really has the disease?
A man has been murdered, and various pieces of evidence mean that we can be certain that the murderer had a particular disease. The disease is rare; only 1 in 10,000 people have it. The suspect has been tested for the disease, using a test that is 99 percent accurate, and the test was positive.
A. 1 in 1: certain B. 99 in 100 C. 1 in 100 D. 1 in 101 E. Less than 1 in 101
In a population of 10,000, on average one person will have the disease and they will test positive.
However, because the test is only 99 per cent accurate, 1 per cent of the remaining, healthy population that is, 100 people will also test positive.
So if the suspect has tested positive, the odds are 100 in 101 (or slightly more than 99 per cent) that he does not have the disease, and is simply the victim of a false positive.
Turning this around, the odds are 1 in 101 that he has the disease.