# Does this probability paradox have a name? [duplicate]

I stumbled over a probability paradox on the internet:

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

A) 25%

B) 50%

C) 60%

D) 25%

Given that "at random" means choosing each option with equal probability, each option had a chance of 25% to be correct. But since there are 2 options with 25% as the solution, we get 50% of being correct. In this case, B) would be correct. But then again, the probability of choosing B) at random would be 25%. And so on.

Does this paradox have a name? Is there something I can read on it?

## marked as duplicate by kingW3, Namaste, zz20s, Smylic, hardmathJun 8 '17 at 17:16

• It's a self-referential paradox, much like "This sentence is a lie". It's popular enough, but I don't know whether it has its own name. – Arthur Jun 8 '17 at 7:35
• How is this a paradox? Would it be a paradox if the choices were A)90% B)92% C) 95% D)98%? Do you consider a multiple choice question to be a "paradox" if none of the listed answers is correct? – bof Jun 8 '17 at 8:28
• @bof the case you've presented wold be 'a question with set of answers not containing the right answer'. The answers in question are also without the right answer (0%), but if we change an answer C)60% to C)0%, then: if the right answer is $k\%\not\in \{0\%,25\%,50\%\}$, then the right answer is 0%, then the right answer is 25%, then the right answer is 50%, then the right answer is 25%... And we obtain a never ending chain – Jaroslaw Matlak Jun 8 '17 at 8:58
• The given question has 0% in the body but the one with 60% is also answered there. – kingW3 Jun 8 '17 at 10:34
• I would say this is not a duplicate, at least not of the linked question, since this question is not about explaining the paradox, but rather a reference request to whether this specific paradox has a name. – Arthur Jun 9 '17 at 20:45

Actually the answer to your question is not contained in possible answers -$0\%$
If the right answer is $k\%\not\in \{0\%,25\%,50\%\}$, then the right answer is 0%, then the right answer is 25%, then the right answer is 50%, then the right answer is 25%...