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Generałowie i statystyka

Posted on: Kwiecień 7, 2014

My favourite example of this story, told about the Italian physicist Enrico Fermi, newly arrived on American shores, enlisted in the Manhattan nuclear weapons Project, and brought face-to-face in the midst of Wordl War II with U.S. flag officers:

So-and-so is a great general, he was told.
What is the definition ot a great general? Fermi characteristically asked.
I guess it’s a general who’s won many consecutive battles.
How many?
After some back and forthe, they settled on five.
What fraction of American generals are great?
After some more back and fourth, they settled on a few percent.

But imagine, Fermi rejoined, that there is no such thing as a great general, that all armies are equally matched, and the winning a battle is purely a matter of chance. Then the chance of winning one battle is one out of two, or 1/2; two battles 1/4, three 1/8, four 1/16 and five consecutive battles 1/32–which is about 3 percent. You would expect a few percent of American generals to winn five consecutive battles–purely by chance. Now, has any of them won ten consecutive battles…?

Carl Sagan, The Demon-Haunted World: Science as a Candle in the Dark, 1995

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