Question 654360: Suppose that 5% of people in society are “nerds”.
Professor R. U. Kidding has spent his lifetime trying to invent a test to easily and quickly determine whether or not an individual is a “nerd”.
The professor has finally invented a screening test. The test, however, is only 85% reliable. Specifically, the test results in false positives 15% of the time. In other words, 15% of the time a test will conclude a person is a “nerd” when they are really not a nerd. However, if the person actually is a nerd, the test will conclude they are a nerd with 100% reliability.
Professor R. U. Kidding has recently administered the test to his good friend Johnny Crabcakes. The test determined that Johnny Crabcakes is a nerd.
Johnny Crabcakes, after hearing the results, said nervously “wow, given the reliability of the test, there is an 85% chance that I am really a nerd.”
Is Johnny Crabcakes right that since he tested positive that there is an 85% chance he is a nerd?
Answer by lynnlo(4176)   (Show Source):
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