If you choose an answer to this question at random, what is the chance you will be correct?
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When limited to the 4 provided answers, there is no correct answer, because this question is a paradox.
When there is one correct answer, the chance to pick that answer would be 25%. However, the answer 25% exists twice, so there is a 50% chance of picking it. But there is only one answer which says 50% and the chance to pick that answer is 25%.
However, there is no instruction in the question that you need to pick one of the provided answers. In that case "picking an answer at random" would mean that I would respond with a completely random statement like "A", "Y", "3.14159", "Warshaw", "jksdaskfa" or "Bob is the one who stole the strawberry cake". My answer could be literally anything, so there is an unlimited number of possible responses. Assuming that there is an unlimited set of incorrect answers but only a limited set of correct answers, the chance of picking a correct answer is
0% which would be my answer.
The obvious answer seems to be 25%, as there are 4 options.
2 of the options are 25%, so there would be a 50% chance of guessing it randomly so it cannot be the correct answer. 1 of the options is 50%, and of course, the chances of guessing this at random are 25% which is also wrong.
The last option is:
60%. If 60% is correct, this means that there is a correct answer and so a 25% chance of getting the correct answer, thus making 60% wrong. However, if the last available option is wrong, then there is a 0% chance of you getting it correct and therefore 0% becomes correct again. This is equivalent to being given the question: "Will you answer "no" to this question? Yes/No?". Regardless of what you say, you are wrong.
A multiple choice question none of whose answers are correct isn't very interesting. If I asked:
What is 3 + 4? a)3 b)4 c)5 c)6
The only sensible answer is:
Is "this is a stupid question". That is essentially what the question does, just in a confusing and paradoxical way by making the question about itself.
This is a stupid question.