More head-busting probability

[kirisutogomen]

rifmeister posts a wonderful little problem here, and it reminded me of an entirely different wacko problem posed on the xkcd balrog bolgia blog "blag". I don't particularly recommend slogging through all the comments, as a reasonable number of them are useless or worse, but the link to the Wikipedia article on the "two envelopes problem" is certainly worth a look.

Comments

[fredrickegerman.livejournal.com]

Yeah, I then tried to back-fill by picking two numbers at random from (0,1). But of course that's just like flipping a coin!

Except for one corner case, which also occurs in the original problem: you can pick exactly the number chosen (with probability 0, of course). Which leads me to wonder if we're not in one of these "integrate a function that's everywhere 0 and get 1" kinds of situations.