Bot is correct. Bayes’ theorem is just wrong. There are two ways I’ll show this. In the above example, you already chose a ball and it came out gold. This means that you chose from either the left (‘G’, ‘G’) or middle (‘G’, ‘S’) boxes. Nothing else is known. There is no chance that you took from the right box (‘S’, ‘S’). There is an equal likelihood that you chose from the left or middle boxes. If you chose from the left box, you choose another gold ball. If you choose from the middle box, you choose a silver ball.
Therefore, the likelihood of choosing a second golden ball is 50%.
Second to that, this outlook hashes out empirically as well. I wrote a script that randomly plays this game 10,000 times and sees how likely one is to choose a gold ball after having already chosen a gold ball. The outcome is always roughly 50%.
tldr bayes’ theorem is wrong
@NEETzsche @pleb@hunk.city @bot @jeffcliff how does this mean bayes is wrong? The only confusion here is over whether you are calculating the probability conditional on your choice or the overall probalility, which is just a matter of how you interpret the language of the question. There is no contradiction of bayes.
Cope.