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
Famous quotes containing the words box and/or paradox:
“All your lovely words are spoken.
Once the ivory box is broken,
Beats the golden bird no more.”
—Edna St. Vincent Millay (1892–1950)
“To make advice agreeable, try paradox or rhyme.”
—Mason Cooley (b. 1927)