Ex. You have a test that detects cancer with 99% certainty, and a prevalence of cancer of 1 in 1 million people. In a sample size of 100 million people:

Ex. You have a test that detects cancer with 99% certainty, and a prevalence of cancer of 1 in 1 million people. In a sample size of 100 million people: People with cancer correctly identified: 99%*100=99 people People with cancer not identified: 1%*100=1 person People without cancer falsely identified= 1%*99,999,900 = 999,999 people People without cancer correctly identified:99%*99,999,900=98,999,901 people Even with 99% accuracy you have nearly a million people falsely identified, but only identify 99 people with cancer. Now extend this to terrorism, 800 million riders for 12 years, and a prevalence of 2? possible terrorists (shoe, underwear) in the last 12 years. Also keep in mind that since both of these guys made it on the plane, the accuracy of the the terrorist screening process may not be too high.