C, which means A or D, which means C, which means...

This seems like a version of the Liar paradox. Assume "this statement is false" is true. Is the statement true or false?

There are a bunch of ways to break the paradox, but they all require using a system that doesn't allow it to exist. For example, a system where truth is a percentage so a statement being 50% true is allowed.

For this question, one way to break the paradox would be to say that multiple choice answers must all be unique and repeated answers are ignored. Using that rule, this question only has the answers a) 25%, b) 60%, and c) 50%, and none of them are correct. There's a 0% chance of getting the correct answer.

50/50, you either guess it right or you dont

If you suppose a multiple choice test MUST ONLY have one correct answer:

1. Eliminate duplicate 25% answers

2. You are left with 60% and 50% as potential answers to this question.

3. C is the answer

If you were to actually select an answer at random to this question while believing the above, you would have a 50% chance of answering 25%.

It is obvious to postulate that: for all multiple choice questions with no duplicate answers, there is a 25% chance of selecting the correct answer.

However as you can see, in order to integrate the answer being C with the question itself, we have to destroy the constraints of the solution and treat the duplicate 25% answers as one sum correct answer.

Do you choose to see the multiple choice answer space as an expression of the infinite space of potential free form answers? Was the answer to the question itself an expression of multiple choice probability or was it the answer from the free form answer space condensed into the multiple choice answer space?

The question demonstrates arriving at different answers between inductive and deductive reasoning. The answer depends on whether we are taking the answers and working backwards or taking the question and working forwards. The question itself forces the inductive reasoning strategy to falter at the duplicate answers, leading to deductive reasoning being the remaining strategy. Some may choose to say "there is no answer" in the presence of needing to answer a question that only has an answer because we are forced to pick one option, and otherwise would be invalid. Some may choose to point out it is obviously a paradox.

Paradoxes aside, if you're given multiple choices without the guarantee that any of them are correct, you can't assign a chance of picking the right one at random anyway.

What's the correct value if the answer is not picked at random but the test takers can choose freely?

Thanks for making me laugh all alone in my car before heading in to work. I wish I could give you an award. Cheers!

The answer is not available. The answer is 0 Percent. Each answer, if chosen, would be incorrect. If 0% was an answer, it would be the correct one despite being a 25% chance. Of course, if one 25% was there, that would be the correct answer.

This only produces a paradox if you fall for the usual fallacy that "at random" necessarily means "with uniform probability".

For example, I would pick an answer at random by rolling a fair cubic die and picking a) if it rolls a 1, b) on a 2, d) on a 3 or c) otherwise so for me the answer is c) 50%.

However, as it specifies that you are to pick at random the existence, uniqueness and value of the correct answer depends on the specific distribution you choose.

I see 25% twice so my bet is on 50%.

33% innit