Given a set of possible actions, you randomly pick one with no reason whatsoever, because you're a fool.
I did my exam by randomly choosing my answers.
A somewhat related word might be babbling, which suggests there is a foolish/nonsensical/dumb element in action. But babbling seems to be too focused on conversations rather than option-picking.
The question Single word for random selection doesn't have answers with the "foolish" element.