Beware, you are making a strong assumption: that the test's accuracy is the same regarding false negatives and false positives. For example, a test may not find enough "anomaly" in an ill person to trigger the positive, thus yielding a false negative; at the same time, it may as well never find any "anomaly" in a sane person, and as a consequence never give any false positive. Back to your example, it's obvious that a test with a 0.01 probability to give a false positive is completely useless for an illness that affects 1e-6 of people.