Bertrand's box paradox is a classic paradox of elementary probability theory. It was first posed by Joseph Bertrand in his Calcul des probabilités, published in 1889.
There are three boxes:
- a box containing two gold coins,
- a box with two silver coins, and
- a box with one of each.
After choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, it may seem that the probability that the remaining coin is gold is 1⁄2; in fact, the probability is actually 2⁄3. Two problems that are logically equivalent are the Monty Hall problem and the Three Prisoners problem.
These simple but slightly counterintuitive puzzles are used as a standard example in teaching probability theory. Their solution illustrates some basic principles, including the Kolmogorov axioms.
Read more about Bertrand's Box Paradox: Box Version, The Paradox As Stated By Bertrand, Card Version, Related Problems, Notes and References
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