Gold Coin in the Box
There are three boxes. One holds two gold coins, one holds two silver coins, and one holds one gold coin and one silver coin. You choose a box uniformly at random and then draw one of its two coins uniformly at random, without looking at the other. The coin you drew is gold. What is the probability that the other coin in the same box is also gold? Give your answer as a reduced fraction.
Related problems & prerequisites
Worth solving first
- Two Children 3.0/10
Source: Bertrand's box paradox, from Joseph Bertrand, Calcul des probabilités (1889). Statement written for AxiomIQ.