This is pressing two letters, and you're explicitly told to press them in a way which feels random (which is going to be culturally determined). Aristotle would say that this is about habit, not free will -- unless you're opting to ignore the instructions.
Can you elaborate on how one's perception of randomness is subject to cultural bias? You do have to realize that frequent runs of repeated characters are expected to appear in a truly random sequence, but that's more a matter of basic reasoning (or perhaps education) than culture.
This might easily be more about formal education in statistics than about culture, though. I'd expect people from any culture we know about to have the intuitive expectations I mentioned -- identifying randomness with chaos.