Although your three scenarios may be pedantically valid, only the first one makes any real sense.
If there are goats behind two of the doors, then Monty opening the door with the car behind it would make for a really stupid game show. He might as well just open the door you chose since both actions tell you that you picked a goat door.
I suppose you could argue that the problem as stated doesn't make it absolutely clear that you *know* that there are two goat doors (or that there are *always* two goat doors).
But as stated, the only reasonable interpretation is the first one (that makes sense for a game show, that fits common sense, not that fits a mathematician's standard for precision).
As for the real Monty saying that he sometimes opened the "car" door, this is true. And that didn't make the real game show really stupid (yes, I'm sure many regarded the show as plenty stupid, but I'm talking stupid beyond sense, not just a matter of taste) because the real show always (or almost always, I haven't personally reviewed every single episode) had one "goat" door (a joke "prize", and no, it wasn't always a goat), one "car" door (a major prize), and one "appliance" door (a minor prize).
That makes for a more complex statistics problem (as it should, being a real game show). But it has little more to do with the problem as stated other than being the likely inspiration for it and, later, the inspiration for its retitling as well.
Also note that Monty had other options besides opening one of the doors. He could have a prize wheeled out and offer you that in exchange for the door. He often pulled cash out of his pocket and offered you that (perhaps in addition to the prize he just wheeled out). It wouldn't have made much sense to call the show "Let's make a deal" without such negotiations. (:
- tye
In reply to Re^8: Marilyn Vos Savant's Monty Hall problem (common sense)
by tye
in thread Marilyn Vos Savant's Monty Hall problem
by mutated
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