Dan,
You keep saying that probability theory does not apply to a single test taker. This is wrong. The laws of mathematics and probability certainly do apply to him. Just because there is a slim chance that his score may not be within our expected range does not mean that these concepts do not apply to this situation. Probability theory accounts for these unexpected results and adequately explains them. This means that he is fully covered by the theory.
You need to revise what you are writing to something more along the lines of "Although, we would expect someone who is guessing to get about half of their answers correct, there is an outside chance that any single test taker's results could be far from what is expected."
I agree with the rest of what you wrote.
To take a gambling example, could you come to Nevada and hit a jackpot on your very first pull of the slot machine handle? Yes, you could. Does this mean that the mathematics that casinos base their business upon does not apply to you when you first walk in the door? No. No one would come in the door thinking, "I can beat the odds because I am a single random gambler and probability theory doesn't apply to me." See how silly that sounds?
PS If they didn't have table limits, I would be down there playing roulette right now!
As for Mark, he is shocked, shocked I tell you, to learn that there is gambling going on here.
