this post was submitted on 10 Nov 2025
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They don't say that the random answer is chosen uniformly (though that is the norm in the field). If we relax that, then we're putting a distribution on these where we want:
P(correct with distribution (a,b,c,d)) = some value shown on A,B,C,D
I don't see any assumption that we will pick using that distribution, so I think this avoids the recursion.
Unfortunately this has too many solutions. If you put a total of 0.25 weight on A and D, then the rest does not matter. If you put 0.5 weight on C, again the rest is irrelevant.
You've added details that aren't in the question. It's like asking what are the odds of rolling a "one" on a 1d4, and then saying "Well, if it's not a fair 1d4, then ..."
... I... I literally talked about this. It's the first words.
What more was needed?
The question is as posed. We have no indication that we should assume a different distribution of "random".
My favorite indication that someone is using a word in an unusual way is that their question has no answer if you interpret it as usual. I reply to you because you argued very nicely that, if this makes sense at all, it must be with a different use of language than we expect.