Probability problems | Probability theory paradoxes
Bertrand's box paradox
Bertrand's box paradox is a veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités. There are three boxes: 1. * a box containing two gold coins, 2. * a box containing two silver coins, 3. * a box containing one gold coin and one silver coin. The question is to calculate the probability, after choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, of the next coin drawn from the same box also being a gold coin. A veridical paradox is when the correct solution to a puzzle appears to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be 1/2, but the probability is actually 2/3. However, this is not the paradox Bertrand referred to. He showed that if 1/2 were correct, it would lead to a contradiction, so 1/2 cannot be correct. This simple but counterintuitive puzzle is used as a standard example in teaching probability theory. The solution illustrates some basic principles, including the Kolmogorov axioms. (Wikipedia).
