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I 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

I 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.

the_af 2y ago
> I do argue that Well, you're wrong. What's worse, the followup by vos Savant clarified this. > In probability theory you can't assume independence of two random variables unless it's a part of the problem statement In most logic puzzles you can safely assume an interpretation of the problem that makes sense and which doesn't go into extraneous tangents. Going "well, akshually, if we assume a spherical goat..." is usually a bad sign. Frankly, all of this still reads as an a posteriori rationalization for finding the solution to the straightforward formulation of the puzzle counterintuitive.
- alexey-salmin 2y ago
  > Frankly, all of this still reads as an a posteriori rationalization for finding the solution to the straightforward formulation of the puzzle counterintuitive Luckily, when I was introduced to that problem many years ago it was presented correctly and the answer albeit counterintuitive was perfectly clear. Developing an intuition for it was also rather easy (what is the chance I guessed incorrectly at a first try? it's the answer). What's above is my reaction to the incomplete formulation of the problem and an incorrect answer that follows. The reason I'm so annoyed by this is because probability theory is very fragile and only works when applied with absolute precision. If you follow your approach with the Two Envelopes Problem and make some "reasonable assumptions", you get a crazy answer (always switch). And people who are in the business of logic puzzles rather than probability theory wouldn't even know the difference. Therefore I would rather discourage people from working on logic puzzles and suggest doing the actual math instead.

the_af 2y ago

> I do argue that Well, you're wrong. What's worse, the followup by vos Savant clarified this. > In probability theory you can't assume independence of two random variables unless it's a part of the problem statement In most logic puzzles you can safely assume an interpretation of the problem that makes sense and which doesn't go into extraneous tangents. Going "well, akshually, if we assume a spherical goat..." is usually a bad sign. Frankly, all of this still reads as an a posteriori rationalization for finding the solution to the straightforward formulation of the puzzle counterintuitive.

alexey-salmin 2y ago
> Frankly, all of this still reads as an a posteriori rationalization for finding the solution to the straightforward formulation of the puzzle counterintuitive Luckily, when I was introduced to that problem many years ago it was presented correctly and the answer albeit counterintuitive was perfectly clear. Developing an intuition for it was also rather easy (what is the chance I guessed incorrectly at a first try? it's the answer). What's above is my reaction to the incomplete formulation of the problem and an incorrect answer that follows. The reason I'm so annoyed by this is because probability theory is very fragile and only works when applied with absolute precision. If you follow your approach with the Two Envelopes Problem and make some "reasonable assumptions", you get a crazy answer (always switch). And people who are in the business of logic puzzles rather than probability theory wouldn't even know the difference. Therefore I would rather discourage people from working on logic puzzles and suggest doing the actual math instead.