But the two choices aren't equally likely, because someone has chosen the amounts in the envelopes through a non-random process. You could make inferences based

But the two choices aren't equally likely, because someone has chosen the amounts in the envelopes through a non-random process. You could make inferences based on what you expect the person to spend on prices, but it's no longer a simple mathematical problem at that point. Which is why the problem as stated doesn't let you look in the envelope before deciding whether to switch or not. Then it's obvious switching makes no difference.