How does one "answer" this? My head is full of fog

It is strongly reminiscent of "This sentence is false. Is that sentence correct?". Basically, if 40% is correct, you have 40% chance. But if 20% is correct, you have 20% chance. But if they are both correct, then there's 60% chance, which gives 0% chance, which gives 20% chance. So 20% wouldn't keep looping around, but 40% wouldn't either, but they can't both be correct. Should we say there is no answer, the question is a liar paradox?

I can't put my finger on what is "wrong" with the question…

If correct is taken to mean (can consistently be correct) then (B), (C), and (E) are possible and (A) is not. But then what about (D)? Could it be "meta-consistently-correct" or something?

More seriously, I would simply say that there is no solution to this question (yes, there is a similarity with the liar paradox). With a slightly different wording (not saying "... the probability ..." which implies uniqueness) there could be two different consistent solutions, 20% and 40%. The cause of the apparent paradox is the self-reference in the question.