[ntucker]

Yeah, I look at it this way: Let's just focus on set B. You're staring at two doors. Some random process decided whether the things behind the doors are a goat and a car (2/3 of the time) or two goats (1/3 of the time). Someone privy to what's behind the doors deliberately opens one to reveal the goat. What changed? Nothing. The random outcome was decided before the door was opened and your odds don't change. That closed door now has a 2/3 chance of having a car behind it.