>>13153252>Depending on which it is, either a single gold ball OR a single silver ball remains to be drawn, thus the probability of your next draw being a gold ball is 50% and can ONLY be 50%.This claim does not follow. Just because there are two boxes that you could have, does not mean the probabilities of having each box are the same. They're not. The probability that you have the box that had two gold coins is twice the probability that you have the box that had just one gold coin. This is because you are given more information than just that you don't have the box that has two silver coins. So you have to calculate the conditional probability, not the prior probability.
This is a very basic example in probability theory called Bertrand's box paradox. You can also just run the experiment yourself, or simulate with some computer code (see pic related).
