False Positive Puzzler

Jun 30, 2001

RAY: Here it is, the new and final Puzzler of this current Puzzler season.

There's a rare disease that's sweeping through your town. Of all the people who are exposed to it, 0.1 percent of the people actually contract the disease. There are no symptoms until the disease actually occurs. However, there's 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 with me?

TOM: I'm with you!

RAY: 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 don't really have the disease.

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


RAY: Let's say if it was 100 people who took it . . . let's start here, Tommy, 100 people.

TOM: No, I'm with you. I was on a different track. I'm with you. Fifty people who take the test will test positive and yet they will not have it.

RAY: Right. So out of 1,000 people who take it . . .

TOM: Yeah.

RAY: OK? And you're included in that thousand.

TOM: Yes.

RAY: OK? 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.

TOM: Correct.

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

TOM: Two percent.

RAY: And that's just another way that statistics can fool and lie to you and make you jump, suicidal . . . and jump off a bridge because you tested positive.

TOM: Sure.

RAY: And the test is 95 percent accurate.

TOM: It sounds so good. So you're saying 2 percent is pretty small.

RAY: Well, I mean, your chances of having it are twentyfold greater than just a person off the street.

TOM: Exactly. Right.

RAY: You know?

TOM: Which is only .1 percent.

RAY: By testing positive.

TOM: Yeah.

RAY: But it's still . . . I mean, considering how dire the news was just a moment ago . . .

TOM: It's now down to 2 percent.

RAY: It's down to 2 percent. I mean . . .

TOM: Don't even pay any attention to it.

RAY: You've got a 2 percent chance of being hit by Skylab. Is that still up there? Anyway, who's our winner?

TOM: The winner is . . . no kidding.

RAY: Jeez.

TOM: What are the chances of this? Wow. The winner is a guy named‹and I'm going to pronounce it correctly for us‹Frank Maggliozi, or, as some people would say, Maggliozi from Rye Brook, New York. Wow.

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