someone's capacity and habits to re-compute a problem's answer, using the algorithmic mind, rather than accept the intuitive default answer that their autonomous mind spits out.

I don't think you could really apply any 'algorithmic' method to that question (other than looking it up, but that would be cheating). It was a test on how much confidence you put in your heuristics. (BTW, It seems that I've underestimated mine, or I've been lucky, since I've got the date off by one year but estimated my confidence at 50% IIRC). Still, it was a valuable test, since most of human reasoning is necessarily heuristic.

most people in the general public don't know Bayes' theorem

Really? What probability do you assign to that statement being true? :D

I'm under the impression that Bayes' theorem is included in the high school math programs of most developed countries, and I'm certain it is included in any science and engineering college program.