Mathematics breaks sometimes when a sentence refers to itself (because it can create contradicting paradoxes). That’s why such sentences are not allowed in formal mathematics.
This example isn’t really a contradicting paradox yet though, none of the answers are correct hence the question is unanswerable (a logical possibility for an arbitrary question). Other commenters correctly pointed out that this setup would be more interesting if 0% would be one of the given possibilities, because then the question is no longer logically unanswerable hence it would be a contradicting paradox (assuming the question is unanswerable implies a possible answer and assuming that a specific one of the answers is correct implies that it’s not correct)
There's no joke; the 4th choice (in addition to 25%, 25%, 50%) is arbitrary; it could be 0%, 100%, or anything other than 25% or 50%. The only purpose it serves is to be a 4th option (thus making the probability of choosing any individual answer 25% when choosing randomly).
The question would work just as well if it had 3 options:
You first think it's 25% because 1/4, then you see there's two 25% options, so 2/4 and now you're at 50%. But wait a minute, now 50% is the right answer so it's 1/4 so 25%...
I'm wondering if the correct answer somehow becomes 60% too since then you could've progressed through all the answers without any of them actually ending up as correct
Logical progression. You see four answers and think 25%. You see two 25%s and think 50%, but then you don’t know how to square that because 50% is there too!
Delightful, had to come to the comments after a minute - certified brain* breaker!
Under the assumption that at least one of those answers is "correct" and fixed (not changing with respect to guesses) and that all options are listed, it is either 25 or 50 percent. 25 if the "correct" answer is either 50 or 60 (or exactly one of the 25's), and 50 if the correct answer is 25.
Clearly this requires a departure from the expected definitions of the words and/or numbers in the question. It's terrible question writing, I'll say.
I'd argue it's 50% by process of eliminating with some grouping. 60% is right out, as it doesn't make sense. This essentially leaves us with 50% and 25%, and since there's 2 options a random guess would have a 50% chance of being correct
Maybe the answer is 100%
Because it depends on how and when you ask/answer.
My opinion:
The question isn't asking you which of the options is the correct answer, it's asking what your odds are of choosing the correct answer. Regardless of the value of the choices.
The question is asking for a value. Not one of the following letter choice.
Without knowing the correct answer, assuming one is correct,, a random guess out of 4 choice answers would be a 1 in 4 chance. 25%
If 25 is the correct blind answer, then, because this prof is trying to be funny, it becomes depending how you look at it, 2 in 4. Which makes it 50 which makes the odds 1 in 4.
Also, by selecting any one the only option is correct or incorrect. So 50/50