I follow you... with four possible choices, there is a 1/4 chance of randomly picking correctly... or 25%. In this case there are two answers that are 25% (A & D), so logic would dictate that you have a 2/4 (or 1/2) chance of randomly picking one of those, hence 50%, so the answer is C as you suggest.
However...
If the correct answer to this question is C, and you are picking an answer to this question at random, there is only a 25% that you select "C" (C = 1/4, A or B or D = 3/4). But if that is the case, then both A & D are correct... therefore we are back to 50% and answer C... which triggers the loop and the cycle continues indefinitely!
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