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The earliest of several probability puzzles related to the Monty Hall problem is Bertrand's box paradox, posed by Joseph Bertrand in 1889 in his Calcul des probabilités. [67] In this puzzle, there are three boxes: a box containing two gold coins, a box with two silver coins, and a box with one of each.
Pages in category "Probability problems" The following 31 pages are in this category, out of 31 total. ... Pill puzzle; Problem of points; S. Secretary problem;
Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set ...
Probability distribution of the length of the longest cycle of a random permutation of the numbers 1 to 100. The green area corresponds to the survival probability of the prisoners. In the initial problem, the 100 prisoners are successful if the longest cycle of the permutation has a length of at most 50.
Each scenario has a 1 / 6 probability. The original three prisoners problem can be seen in this light: The warden in that problem still has these six cases, each with a 1 / 6 probability of occurring. However, the warden in the original case cannot reveal the fate of a pardoned prisoner.
A single ball is then drawn from the box. In this setting, the question from the original problem resolves to one of two different questions: "what is the probability that a green ball was placed in the box" and "what is the probability a green ball was drawn from the box". These questions ask for the probability of two different events, and ...
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