The following faulty reasoning appears to give a probability of 1 / 2: What is the chance of the coin on the other side being gold?
A box is chosen at random, a random drawer is opened, and a gold coin is found inside it. One box has a gold coin on each side ( GG), one a silver coin on each side ( SS), and the other a gold coin on one side and a silver coin on the other ( GS). The problem can be reframed by describing the boxes as each having one drawer on each of two sides. Thus, the overall probability of drawing a gold coin in the second draw is 0 / 3 + 1 / 3 + 1 / 3 = 2 / 3. The probability of drawing another gold coin from the same box is 0 in (a), and 1 in (b) and (c). The solution illustrates some basic principles, including the Kolmogorov axioms.īertrand's box paradox: the three equally probable outcomes after the first gold coin draw. This simple but counterintuitive puzzle is used as a standard example in teaching probability theory. He showed that if 1 / 2 were correct, it would lead to a contradiction, so 1 / 2 cannot be correct. However, this is not the paradox Bertrand referred to. It may seem intuitive that the probability that the remaining coin is gold should be 1 / 2, but the probability is actually 2 / 3. 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.Ī veridical paradox is when the correct solution to a puzzle appears to be counterintuitive. a box containing one gold coin and one silver coin.It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités. The paradox starts with three boxes, the contents of which are initially unknownīertrand's box paradox is a veridical paradox in elementary probability theory.
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