> The reasons why the original problem is so confusing is the same reason why the Monty Hall is so confusing: people have different understandings of the question, and don't realize it in discussions.

I think this is true of the "children" question, but I actually disagree that this is what makes the Monty Hall question so confusing.

For one thing, I vaguely recall this being asked directly, and even after people agree on all the definitions explicitly, they still consider the answer wrong. (See e.g. some mathematicians like Erdos refusing to believe the correct answer without actually running simulations on computers... by that point you clearly have a real definition.)

For another, when I personally talk to people about Monty Hall, even after I explain the correct answer, and explain all the nuances, people tend to still have a hard time accepting the correct solution and claim to find it counterintuitive (as did I!).

The typical Monty Hall formulation has similar ambiguity because it’s not clear whether or not the host knows the right door. Just like in this question, it’s not clear if the “narrator” knows the first child is a girl.

(Also, this problem has an additional layer of ambiguity where “birth order is irrelevant,” but MF and FM are treated as distinct items in the probability set. Is the order irrelevant to the probability, or is it impossible to distinguish the age of the two children? It would be clearer to simply say “each birth is an independent event.” One of the comments on the blog explains this better than I can.)