4 ms·
The original wording was "You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat." I thin
by dllthomas 2y ago
The original wording was "You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat."
I think there's a good argument that the intended interpretation should be the favored one. If he doesn't use the knowledge to always reveal a goat, why did they bother specifying that he has the knowledge?
But it still doesn't quite explicitly say that he's not picking randomly.
- penteract 2y agoWhat if he used the knowledge to decide whether or not to open a door and offer you the choice? I think that scenario is why most people instinctively want to not switch (even if they aren't consciously aware of it), so it's a pity to disregard it.
- the_af 2y agoPeople instinctively want not to switch because the probabilities involved aren't intuitive. Notice if Monty uses the knowledge of whether to open the door based on what you choose, he'd be giving the whole game away, so that's not it.
- the_af 2y agoIt seems to me you're answering your own question. There's only one reasonable interpretation; you have to go out of your way (unreasonably!) to find any ambiguity.
- dllthomas 2y agoNah, there's a lot of space between "this should be the favored interpretation" and "this is strictly implied" - especially in the context of a math puzzle!
- the_af 2y agoI don't think there is. This is a simple brain teaser. It's fun because the right answer is counterintuitive, that's all. It's not at all about "rules lawyering" the premise of the puzzle.
- alexey-salmin 2y agoBut this makes no sense. You're proving the "counterintuitive answer" with the probability theory but when confronted with the fact that your proof is not mathematically correct you say "this is a simple brain teaser". I don't see how it changes anything. If you rely on the probability theory then you have to do it correctly, there's no special brain teaser version of math. It's like going around saying that "counterintuitive answer to equation x/x=1 is 17" and then "prove it" by dividing 17 by 17 . When confronted with the fact that in math to solve an equation is to find ALL solutions and not just one, you say "It's not at all about rules lawyering the premise of the puzzle". Well avoid dealing with the math then because the math in fact is all about the rules.
- the_af 2y ago> But this makes no sense. You're proving the "counterintuitive answer" with the probability theory but when confronted with the fact that your proof is not mathematically correct you say "this is a simple brain teaser" The answer IS mathematically correct. It's just counterintuitive and it made some PhDs trip. Nobody here -- not even you, before -- was arguing it's mathematically incorrect. Some people, when told the right answer, claimed the problem is underspecified and admits more than one context that may change the answer, which is not at all the same as saying the answer is mathematically incorrect! Not even Diaconis, the person some of you are so eager to defend (for some bizarre reason) claims it's "mathematically incorrect"! It seems you're grasping at straws now.
- alexey-salmin 2y agoI do argue that. In probability theory you can't assume independence of two random variables unless it's a part of the problem statement because this assumption changes everything. Where I got my degree this would be considered an error and an incorrect solution to the problem. It's not different from how in middle school you can incorrectly assume that "x is positive" when solving x^2=4 in R. An answer "x=2" is mathematically incorrect.