Yes. But I do think that thinking critically about the assumptions you are making, in particular that you can meaningfully talk about what it means to pick a random individual in a uniform fashion, is worthwhile for understanding a fair bit of probability and related issues which are relevant in broader in contexts.
As to critically understanding what it means to pick a random individual in a uniform fashion, yes it is worth understanding what one means, as a tremendous amount of mischief is done in the name of randomness. With a finite number of prisoners, I would actually not need to pick prisoners randomly in order to gather statistics. If I would simply count up all the prisoners who got the hat color correct and all that got it wrong, and I do the experiment say 100 times and plot a histogram of the results and then decide whether the results deviate from a nor...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.