BERTRANDS: Paradox in Probability Theory with Video

WHAT IS RANDOM?

By Staff Reporters

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Bertrand’s Paradox is a problem within probability theory first suggested by the French Mathematician Joseph Bertrand (1822–1900) in his 1889 work ‘Calcul des Probabilites’. It sets a physical problem that seems very simple but leads to differing probabilities unless its procedure is more clearly defined.

Based on constructing a random chord in a circle, Bertrand’s paradox involves a single mathematical problem with three reasonable but different solutions. It’s less a paradox and more a cautionary tale. It’s really asking the question: What exactly do you mean by random?

IOW: According to Dan Ariely PhD, two players reaching a state of Nash equilibrium both find themselves with no profits gained via exploitation.

Consequently, over the years the Bertrand paradox has inspired debate, with papers arguing what the true solution is: www.bertrands-paradox.com.

Update: The people from Numberphile and 3Blue1Brown produced a video on YouTube describing and explaining the Bertrand paradox.

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