As a side-note, the maximum entropy principle would tell you to choose the maximum entropy prior given the information you have, and so if you intuit the information that the balls are likely to be produced by the same process, you’ll get a different prior that if you don’t have that information.
I.e., your disagreement might stem from the fact that the maximum entropy principle gives different answers conditional on different information.
I.e., you actually have information to differentiate between drawing n balls and flipping a fair coin n times.
As a side-note, the maximum entropy principle would tell you to choose the maximum entropy prior given the information you have, and so if you intuit the information that the balls are likely to be produced by the same process, you’ll get a different prior that if you don’t have that information.
I.e., your disagreement might stem from the fact that the maximum entropy principle gives different answers conditional on different information.
I.e., you actually have information to differentiate between drawing n balls and flipping a fair coin n times.