via reddit.com
I think the difficulty is that it looks like a math problem,
but since the game-show host *knows* which door has the sports car, and
is taking care not to reveal it ahead of time, it’s not random. It’s really more
like a psychology problem.
I once saw someone explain it by saying “Ok, if there were *ten*
doors, you picked one, and then the host opened all but one of the nine
remaining doors, you’d be pretty quick to switch your choice to that door they carefully
avoided opening, wouldn’t you?”