1). Thanks for an answer, though I don’t think you should ‘tell’ people to “Take a course in probability and statistics.” just because they didn’t understand the logic of one simple question everyone on Earth seems to get wrong. If you didn’t mean it insultingly you should have just ‘suggested’ that ‘I might like to take a course like that’ because ‘you found it helpful and interesting’. Something along those lines at least. You came across like you were insulting me.
Again.. it’s the internet so I don’t really know for sure how you meant it and have to guess.
2). You wrote -“Your error is in assuming that Monty Hall doesn’t know what door has the goat and what door has the car. He isn’t randomly choosing.-”
But isn’t it actually ‘your’ error in assuming it ‘isn’t’ random? Because I promise you I was NOT assuming whether he knew or not…since the ‘story’ doesn’t say. It’s not enough for me that it kinda, sorta, maybe, implies it.
Maybe that’s my problem with it? And that’d be an issue unrelated to the math of it exactly as I suspected?
If anything, I’d be more inclined to think he didn’t know and it was random.
I also mentioned Harris’s footnote that expands the number of doors just like you mentioned. He even used 1,000 doors rather than your 100. In that example it makes it ‘appear’ that Hall ‘must know’ which door the winner is behind based on the improbability of revealing all losers and ending up with only 2 doors.
BUT… I think that just confuses the issue of the ORIGINAL and only scenario actually in question. I don’t have a problem with that follow-up example. I don’t think it is logically the EXACT same problem though.
Also as I already wrote, the result of the 3 door gamble ‘could have been’ that Hall opens a ‘winning’ door that you didn’t pick and the game is over right there. Essentially that would be accepting your first attempted pick and they are just showing what’s behind doors you didn’t pick for whatever reason.
NOTHING in the story says that couldn’t have happened. It seems like you’re telling me (as well as Sam in his book) to accept a fact not in evidence (that Monty knows where the ‘winner’ is). That’s ‘faith’. Something Sam (and all his fans) is logically against.
Let me ask this then…say the ‘winning’ door is the one you first picked (but they didn’t reveal). Then, IF Hall knows that’s the right door (which you say he in fact does), isn’t it random which of the two ‘loser’ doors he opens?
Wouldn’t that make the result either a 1 out of 2 chance, OR…a 2 out of 3 chance, DEPENDING ON…if your first uncounted attempt actually had the ‘winner’?
Maybe the story just needs to be slightly re-worded? Or would you claim it doesn’t need to be changed at all?