GG would produce a gold coin is 1. The probability that SS would produce a gold coin is 0. The probability that GS would produce a gold coin is . Initially GG, SS and GS are equally likely . Therefore, by Bayes rule the conditional probability that the chosen box is GG, given we have observed a gold coin, is: The correct answer of can also be obtained as follows: Originally, all six coins were equally likely to be chosen. The chosen coin cannot be from drawer S of box GS, or from either drawer of box SS. So it must come from the G drawer of box GS, or either drawer of box GG. The three remaining possibilities are equally likely, so the probability that the drawer is from box GG is . Alternatively, one can simply note that the chosen box has two coins of the same type of the time. So, regardless of what kind of coin is in the chosen drawer, the box has two coins of that type of the time. In other words, the problem is equivalent to asking the question "What is the probability that I will pick a box with two coins of the same color?". Bertrand's point in constructing this example was to show that merely counting cases is not always proper. Instead, one should sum the probabilities that the cases would produce the observed result; and the two methods are equivalent only if this probability is either 1 or 0 in every case. This condition is correctly applied in the second solution method, but not in the first. The paradox as stated by Bertrand It can be easier to understand why is incorrect, if you consider the paradox Bertrand used. After a box has been chosen, but before a drawer is opened, there is a probability that the box has two of the same kind of coin. So, if you then select a drawer at random, before you open it the probability that the other drawer has the same kind of coin is . Opening the drawer that you selected cannot change that. Experimental data In a survey of 53 Psychology freshmen taking an introductory probability course, 35 incorrectly responded ; only 3 students correctly responded . Related problems Other veridical paradoxes in probability include: Boy or Girl paradox Monty Hall problem Three Prisoners problem Two envelopes problem Sleeping Beauty