Either 33 and 1/3% or 12.5% depending on whether the correct answer is either of the other two numbers or one of the copies respectfully.

But that only considers if there's one correct answer of the four. Otherwise there can be anywhere from 2-4 correct answers or no correct answers at all which presents an additional 12 possibilities with either a 20% chance (none of the above as an unlisted or imaginary option E), a 16 and 2/3s% chance (if it's a combination of any two non imaginary choices), a 25% chance (if it's a combination of any three non imaginary choices), or a 100% choice (since all non imaginary choices must be taken anyways) and for the sake of the argument (and not having the options and probability spiral out into infinity) are all considered imaginary numbers like the ones in the paragraph above.

The tl;dr is that all the choices are bald face, dirty liars and that you've either have a 33.33ect% chance, a 25% chance, a 12.5% chance, or a 0% chance to get it right (which effectively equals a 25% chance).

Er...no. This is completely wrong. Well, you're right that the question doesn't have a right answer, but certainly not for the reasons you gave. If this was a free response section of a test I was grading you would get 0 points.

The question is ill-formed. The answer to the question depends on the answer to the question. It is certainly fun to think about, though. We can at least test the logical consistency of each possible answer.

Is it 25%? Well, there are two out of four responses that say 25% so the odds of that are 50%. It fails.

Is it 50%? There is one out of four responses that says 50% so the odds of that are 25%. It too fails.

There is a reason I changed C) from the original. This version is much more fun. In the original one might be tempted to conclude that the chance is 0% since none of the other choices work. Now 0% is a choice! But there's a 25% chance of choosing it, meaning it isn't logically consistent either...

Of course, if you think the 'true' answer is anything not on the list then the odds of selecting it become 0% and that's

*on* the list, so that doesn't work...

Just for fun, here is a variation:

If you choose an answer to this question at random, what is the chance that you will be correct?

A) 25%

B) 50%

C) 100%

D) 50%

Same principle, of course, but now you have multiple 'correct' choices...

Except that what you just said has absolutely nothing to do with what I said past the fact that we're looking at the same problem. What I said completely disregards what the question says because the question is a dirty liar. The point is that the question is no longer about the mathematics posited by the question but the fact that the question has only four viable answers with a degree of uncertainty stored therein.

You have four choices A, B, C, & D; two of which are labeled identically but exist in different points and basically possess the clone conundrum where clones are not identical once they cease to share the same memories, the same building blocks, and the same points in space and time (and I REALLY don't want to go into this clusterfuck). Then it's a matter of the uncertainty of whether the question expects you to take one of the 25%s, both 25%s, one of the other choices, or neither as the question is pulling a Kobeyashi Maru on you leaving an undefined choice E.

The tl;dr is that trying to solve the posed question is bullshit since it's one of those illogical questions used to fry robot processors; thus you're left with either one of two possibilities for half of the possible answers being correct, both possibilities for half of the possible answers being correct, one of the two remaining possibilities being correct, or having no correct solution at all.