Answer to June 3, 2002 Problem
From Click and Clack, The Car Guys

False Positive Problem

 
There’s a rare disease that’s sweeping through your town. Of all the people that are exposed to it, 0.1 percent of the people actually contract the disease. There are no symptoms until the disease actually occurs, but there is a diagnostic test that can detect the presence of the disease up to a year before it strikes. So you could actually seek treatment.

You go to your doctor and he administers the test. It comes out positive. You say, "I’m done for!"

Then you get a little bit encouraged. You say, "Wait a minute, doc, is this test 100 percent accurate?" Your doctor responds, "Well, not really. It’s 95 percent accurate." In other words, 5 percent of the people who take the test will test positive but they won’t really have the disease.

Here's the question: What are the chances that you actually have the disease?

 

Solution to Problem:

Your chances are 1 in 51 (or less than 2 percent).

Only 0.1 percent of the people who were exposed to it actually get it. That's one in a thousand. Now, you tested positive and you figure, I'm done for, especially when you find out the test is 95 percent accurate. But if it is 95% accurate, that means if 1,000 people take the test, 50 people who don't have the disease will test positive.

Fifty-one people out of 1,000 are going to test positive. One of those people is going to have it and 50 are not going to have it.

So your chances of actually having it, even though you tested positive, are one in 51, or a little less than 2 percent.


Correctly solved by:

1. Rick Jones Kennett Square, Pennsylvania
2. Keith Mealy Cincinnati, Ohio
3. James Alarie University of Michigan -- Flint, Michigan
4. Walt Arrison Philadelphia, Pennsylvania
5. Amy Lamport Rockford, Michigan