In medical terms, state A represents a disease or condition for which we are testing. Paul tested positive. A manager decides that next year the company should launch a new product, unless next year is a recession. Further examination shows that the economist has indeed correctly forecast four out of the last five recessions. However, he has also forecasted a recession three times in ten years which did not have recessions.
Recessions occur about one year in four.
Blood found at the scene of a crime has an attribute that occurs in the blood of only one person in a million. According to a test of Jones' blood, he has that attribute. When the court tests the reliability of the witness under circumstances similar to those on the night of the accident, he correctly identifies the color of a cab 80 percent of the time and misidentifies it the other 20 percent. Examining the two cases of a positive diagnosis, it is easy to see that, since they are equal, the proportion of false positives is .5. Most people are surprised to learn that, though the test raises the suspicion that Paul is a user, he is equally likely to be accused falsely.