If I'm stated to be picking an answer at random, in what sense am I choosing?
This seems like an observation about either pointers or Meta-questions. If I pick an answer to {an unspecified thing}, what is the probability of being right?. Choose A/B/C/D.
First, I have to assume the {unspecified thing} is your question itself. Then model a clone of your question, then based on the answers to the clone model, answer your real question. Then I have to make some assumptions about the biases in my random selector (i.e. it has none and picks each option on average 25% of the time). Then I have to make some assumptions about whether one of the answers is right and three are wrong, or if more than one can be right.
If I assume one is right and three are wrong, then A and D are ruled out, so the right answer must be B or C. C can't be right, so it must be B, so my chance of picking "B" and getting the right answer is 25%. So I answer your real question either A or D.
If I assume that A or D could be right, then I assume B and C are wrong and get a 50% chance of picking correctly, so I answer your real question B.
I guess I could carry on and say "if no answer is right and I always pick one of the four, then I have no chance of answering correctly and answer your meta-question with C" and then see if I can sum up all the potential assumption answers and see if it resolves to a most likely sum-over-histories style answer.
But that sounds like work.