Why People Probably Don't Understand Probability Robert Siegel talks with Columbia statistics professor Andrew Gelman. Gelman is the co-author of the book Teaching Statistics: A Bag of Tricks, which includes an age-old statistics experiment that demonstrates how people misunderstand probability when it comes to the coin toss.

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Why People Probably Don't Understand Probability

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ROBERT SIEGEL, host:

Now, one last story arising from last Sunday's Super Bowl, the story that addresses the question how improbable is the improbable? This is not about the rarity of running back the opening kickoff for a touchdown or scoring however many points or missing a field goal or even having two African American coaches competing for the first time. Those things all involved skill or prowess or even bias. This concerns the one thing that happened at the Super Bowl that was a case of pure chance - the coin toss.

(Soundbite of Super Bowl game)

Unidentified Man: Indianapolis calls tails.

(Soundbite of cheering)

(Soundbite of cheering)

Mr. JIM NANTZ (Newscaster, CBS Sports): Well, the odds are more than 1,000-one but that's now 10 straight Super Bowls the NFC has won the coin toss.

SIEGEL: That's the voice of Jim Nantz of CBS Sports pointing out that for the 10th year in a row, the National Football Conference champion, as opposed to the American Football Conference champion, won the coin toss at the Super Bowl to see who would receive first. It's the sort of run of luck that gives rise to talk of jinxes or curses or impossibilities. And it lead us to a lesson in statistics that is related among other places in the book "Teaching Statistics: A Bag of Tricks" by Andrew Gelman and Deborah Nolan.

Andrew Gelman is a professor at Columbia University, joins us from New York City. Welcome to the program, Professor Gelman.

Professor ANDREW GELMAN (Columbia University): Glad to be here.

SIEGEL: Tell us about the experiment that involves tossing coins and also pretending that you're tossing coins.

Professor GELMAN: As a way of giving students an intuition into randomness, we divide the class and then I leave the room. One half of the class has to create a sequence of 100 coin flips, and then they're told to write it on the blackboard as a sequence of zeros and ones.

The other half of the class was instructed to create a fake sequence of 100 zeros and ones that's supposed to look like coin flips.

SIEGEL: And then you return from outside the room.

Professor GELMAN: Yeah. I returned and what I see is two blackboards, each with sequence of 100 zeros and ones, and I can immediately tell which is which.

SIEGEL: You can immediately tell which is the blackboard that represents a real series of 100 events.

Professor GELMAN: Right. A real sequence of coin flips is likely to have a long run of heads or tails. You're more likely than not to see a run of seven straight heads or seven straight tails. The fake sequence, they tend to alternate too much between heads and tails, so I can immediately see the fake one looks too random and the real one looks like something strange went on.

SIEGEL: The stranger the realer, as it turns out. It explains, in part, why some people are surprised by runs of chance and luck in reality and rush to supernatural, even miraculous explanations of things.

Professor GELMAN: No, exactly. The other thing is most things in life aren't coin flips. And so, if you really see a long run of something happening, maybe there is a real reason. The coin flips are just an interesting laboratory for it because it is purely random.

SIEGEL: We did hear, by the way, in that broadcast of the Super Bowl, Jim Nantz, saying the odds are over 1,000 to one. Had he done his homework properly and does he get an A?

Professor GELMAN: I'll give him a B. The chances are 1,024 to one of getting 10 straight one side winning. But then there's another chance of 1,000 to one that the other side could have won all 10. And then there's another chance of 1,000 to one that could have been 10 straight tails. And then there's another chance of 1,000 to one that could have been 10 straight heads. So that gives you a chance of 250 to one that one of those things would happen, which, you know, is maybe a little surprising, but certainly not so shocking either.

SIEGEL: Well, I'll just say that for people who at this moment wish they had a roll of pennies in hand to go and do the experiment, there is a Web site that does generate random coin tosses for you. And there's a link to that Web site at our Web site, NPR.org.

Professor Gelman, thank you very much for talking with us.

Professor GELMAN: Oh, thank you. It's a pleasure.

SIEGEL: Andrew Gelman is a professor at Columbia University who teaches both statistics and political science.