Attack of the Bucolic Plague

Jun 07, 2004

RAY: This puzzler came to us a while ago-- January 1999, to be precise. It's from Professor Bruce Robinson at the University of Tennessee in Knoxville.

Of course, I had to make a few modifications...

TOM: He won't even want to be associated with it, once you're finished.

RAY: I'm sure he'll send us an e-mail asking to have his name expunged.

Here it is:

"A dreaded new disease is sweeping across the countryside. It's called 'The Bucolic Plague.' If you're afflicted with it, you begin wandering around the woods aimlessly, until you finally collapse and die. The remedy is to lock yourself in the bathroom for two or three days, until the urge passes.

"A test has been developed that can detect whether you have the disease. The test is 99 percent accurate. That is, if you have the disease, there is a 99 percent chance that the test will detect it. If you don't have the disease, the test will be 99 percent accurate in saying that you don't.

"In the general population, 0.1 percent of the people have the disease-- that's one-tenth of one percent.

"You decide to go for the test. You get your results: positive."

Should you lock yourself in the bathroom and ask for a constant supply of magazines, or should you not be worried?

And, the real question is, what is the probability that you actually have the Bucolic Plague?

RAY: The real question is if the test comes back positive what is the real probability that you actually have the bucolic plague?

Let's say that where you live there are a million people, and .1 percent, or a thousand people out of a million, have the disease.

If the 999,000 disease-free people are tested, the results will say that one percent of them, or 9,990 have the disease when, in fact, they don't.

TOM: They're misdiagnosed!

RAY: Correct. And of the thousand people who do have the disease, the test results will say that 99 percent of them, or 990 have the disease. So we have a total of 10,980 positive results.

But, we know that out of a million people, only a thousand people really do have the disease. So, the chance that you have Bucolic Plague if you test positive is about one in eleven, or less than 10 percent.

The moral of the story is this: You shouldn't lock yourself in the bathroom, unless you have some really good magazines. Do we have a winner?

TOM: Of course! The winner is Jean Gaska from Shelbyana, Kentucky. For having her answer selected at random from all the correct answers that we got, Jean gets a twenty six dollar gift certificate to the Shameless Commerce Division of, where she can choose from a wide array of fine quality Car Talk junk.

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