Self-referential multiple-choice question

Question

I came across this question, which I believe cannot be satisfactorily answered, but I'm not completely sure. Can you tell me if it has a answer?

If you choose the answer to this question at random,
what is the chance that you will be correct?
a) 25%
b) 50%
c) 60%
d) 25%

Possible duplicate of Multiple-choice question about the probability of a random answer to itself being correct (for reviewers: only option (c) is different from the duplicating target, but 60% clearly doesn't make more sense than 0%) — YuiTo Cheng, Apr 07 '19 at 09:35

score 3 · Answer 1 · answered Apr 07 '19 at 06:47

Correct (on the typical assumptions we can only pick one answer, that the selection is uniformly random, etc.). The question is actually a fairly common paradox. The cause is the sort of self-referential nature of the question.

Typically for multiple-choice questions with four answers, at random there is a $25\%$ chance to get it right. But two answers have that choice.
So logically it would be $50\%$, but only one choice corresponds to that. So you're damned if you pick either one: if $50\%$ is correct, the odds are $25\%$ and if $25\%$ is correct the odds are $50\%$.
$60\%$ simply makes no sense, being not a multiple of $25\%$, and can be ruled out outright.

So as it is posed, there is no correct answer.

Self-referential multiple-choice question

1 Answers1