Originally Posted by omk3
Okay, just thinking aloud, so you're safe to click it:
I'll address some of your thoughts, just the clarify things that might not have been perfectly clear in the problem statement.
(i) the 45/55 split is just random chance. The problem still works with any similar numbers, e.g. 35/65, 50/50, 51/49, etc. The exact answer might be a little different though.
(ii) probability arguments won't help. The prisoner can't be 99% or 99.9% or even 99.99999% certain. The prisoner must be able to prove that they know their ink colour by a process of logical deduction.