How To Make Sense Of Bertrand’s Box Paradox?

This Paradox features a counterintuitive probability puzzle!

Hemanth
Street Science

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How To Make Sense Of Bertrand’s Box Paradox? — Three boxes are placed side by side. Box 1 contains 2 gold coins. Box 2 contains one silver coin and one gold coin. Box 3 contains 2 silver coins.
Bertrand’s Box Paradox — Illustration created by the author

Joseph Louis François Bertrand was a genius French mathematician who lived in the 19th century. By the time he was just nine years old, he had already lost his father. But even at that age, Bertrand could speak Latin fluently and was well-versed in mathematical concepts.

A black and white portrait of Joseph Louis François Bertrand — Image courtesy of Wikimedia Commons
Joseph Louis François Bertrand — Image courtesy of Wikimedia Commons

Between the ages of eleven and seventeen, he completed two bachelor’s degrees and a PhD in the mathematical theory of electricity. He went on to make significant contributions in the fields of number theory, probability theory, differential geometry, economics, and thermodynamics. Among many other things, he was the first to define real numbers using a notion that we now refer to as a Dedekind cut.

In 1889, Bertrand published his work titled “Calcul des Probabilités”, in which he wrote about a counterintuitive paradox involving probability. It starts with a simple puzzle.

How To Make Sense Of Bertrand’s Box Paradox? — Three boxes are placed side by side. Box 1 contains 2 gold coins. Box 2 contains one silver coin and one gold coin. Box 3 contains 2 silver coins.
Bertrand’s Box Paradox — Illustration created by the author

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