Sure! The original problem invites assumptions of symmetry and integrality[1] and so on, and the implied assumptions result in a fully specified probability model. The adjusted problem adds information that necessarily breaks symmetry, and there is no correspondingly “obvious” set of assumptions that leads to a unique answer.
So yes, communicating probability problems requires some shared concepts and assumptions just like communication about anything else. I’ve previously commented here about my experience with word problems in teaching mathematics, and how the hardest part is not anything to do with the mathematics itself, but with background assumptions about interpreting the problem that were not explicitly taught.
I agree that there isn’t an “obvious” set of assumptions for the latter question that yields a unique answer. And granted I didn’t really dig into why entropy is a good measure, but I do think it ultimately yields the unique best guess given the information you have. The fact that it’s not obvious is rather the point! The question has a best answer, even if you don’t know what it is or how to give it.
Sure! The original problem invites assumptions of symmetry and integrality[1] and so on, and the implied assumptions result in a fully specified probability model. The adjusted problem adds information that necessarily breaks symmetry, and there is no correspondingly “obvious” set of assumptions that leads to a unique answer.
So yes, communicating probability problems requires some shared concepts and assumptions just like communication about anything else. I’ve previously commented here about my experience with word problems in teaching mathematics, and how the hardest part is not anything to do with the mathematics itself, but with background assumptions about interpreting the problem that were not explicitly taught.
The original problem never said that the random number generator only gives integers in the range 1 to 6. That’s an additional assumption.
I agree that there isn’t an “obvious” set of assumptions for the latter question that yields a unique answer. And granted I didn’t really dig into why entropy is a good measure, but I do think it ultimately yields the unique best guess given the information you have. The fact that it’s not obvious is rather the point! The question has a best answer, even if you don’t know what it is or how to give it.