Problem:
Suppose that one of every people in a certain population has a particular disease, which displays no symptoms. A blood test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, there is a false positive rate - in other words, for such people, of the time the test will turn out negative, but of the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let be the probability that a person who is chosen at random from this population and gets a positive test result actually has the disease. Which of the following is closest to ?
Answer Choices:
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Solution:
On average for every people tested, will test positive because he or she has the disease, while will test positive even though they do not have the disease. In other words, of approximately people who test positive, only has the disease, so the probability is approximately .
The problems on this page are the property of the MAA's American Mathematics Competitions