Consider Derek's example of a disease that affects one person in a thousand. The test was 99% accurate, meaning one false positive for every hundred people, or 10 in a thousand. So 11 people would get positive tests but only 1 is real. So the odds of being the real one are 1:11 or 9%. Suppose there is a new test that is 99.9% accurate; ten times more accurate. Compared to the first test, a positive result on the second test would indicate that the probability that you have the disease is