I once had a book of puzzles, which posed this question (paraphrased):
Alice likes tea. She has a box containing 100 teabags. The teabags come in twos (that is, two teabags are attached to each other). Every day, Alice makes a cup of tea with the teabags. She would reach into the box of teabags and pick something out. If she picks a teabag that's attached to another, she uses one of them and tosses the other back. If she picks a single teabag, she uses that only. When the box is empty (i.e. 100 days have passed), she buys a new box of 100 teabags (50 $\times$ 2).
One day Alice goes on holiday. When she returns, she's completely forgotten how many teabags she's used. As she is reaching into the box of teabags, she wonders if she's more likely to draw out two teabags or one. She reasons: because two teabags are physically bigger than one, I'm more likely to draw out two teabags.
Is her thinking reasonable?
I don't have the book anymore, but I vaguely remember the solution as her thinking is not reasonable. Because there's no prior at all, both outcomes are equally likely, and the probability of either is 50%.
Is the book's argument correct? It seems counterintuitive to me: because Alice has no idea how many teabags she's used, probability theory can't even begin to attack the problem. From that, since probability theory is inapplicable, one might as well use physics reasoning and therefore Alice's thinking is reasonable.