Interesting. My first 'intuition' was that, since there's 2 doors remaining, they each have a 50% chance of having the car behind them, so it doesn't matter which one I pick. But then I started thinking, if we make it into a rule that the 'talk show host' changes the door randomly after your first choice, then this might influence the chances somehow, though I could not specify how by just superficially thinking about it without math.
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Yeah, if he changes the door randomly, it would have been more complicated than this, and this would then likely involve the application of combinatorics, to calculate the total possible ways for the probability (I might probably not have even bothered racking my brain over such a situation).