
Unanswerable multiple choice question - yaroslavvb
If you choose the answer to this question at random, what is the chance it will be correct?<p>A) 25%  B) 50%  C) 0%  D) 25%
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david
Well, any multple choice question is going to be unanswerable if none of the
choices given are a correct answer.

Since I think most would define a multiple choice question as one with a list
of answers from which you pick the correct one, I say this question fails to
validate.

Thus not only is this multiple choice question unanswerable, it's not even a
multiple choice question. Try wrapping that around your head.

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pook
It is answerable... with a swift kick to the balls of the person asking it.

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kqr2
But there's only a 50% chance that the person asking that will have balls.

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ZachPruckowski
I would speculate that of the people to ask annoying trick questions, the vast
majority of them are smug males.

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stcredzero
There are lot a of females who like to deflate smug males with trick
questions.

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ZachPruckowski
Hahaha, fair enough.

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goodside
A more distilled version:

Which of the following is the answer to this question?

A) B

B) A

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yaroslavvb
Except here you could say "both are correct" or "neither are correct", whereas
in the original question those also cause a paradox

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sqrt17
Since A and D give you the same result, the question is a "check all that
apply question". Excluding contradictory combinations, there are four answers:

* nothing checked (i.e., none of A,B,C,D)

* A+D

* B

* C

Assume the correct choice is among these four answers (it is, since we also
include a "none of these" option); then you have a one-in-four chance to get
it right. Hence, A+D is right.

If this is not a "check all that apply" question, then having both A and D is
contradictory and the person posing this question deserves a whack on the
head.

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danteembermage
Completely different question:

This question is posed to a large number of people who all attempt to answer
is correctly. "What fraction of respondents answered the same as you? a) 25%
b) 50% c) 0% d) 25%"

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

What if you change it to "What fraction of respondents not including you
answered the same as you"?

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cb18
Where is correctness defined?

What is the antecedent for 'it,' the 'answer' or the 'question'?

Does this phrase even make sense? I suspect it is supposed to be some
'recursive cleverness,' or just not make sense?

C) 0% because for something to be correct it follows that it fits a given
definition of correctness of which none is given.

now the recursion has started to work based on the above reasoning

So if C)0% is the "correct answer"(that is, there is no correct answer) then
choosing an answer at random will be correct 25% of the time, if you shift to
viewing 25% as the "correct answer" then you have a 50% chance of randomly
selecting a "correct answer"

what is the chance [the question] will be correct? C)0%

q1=what is the chance [the question] will be correct?

what is the chance [an answer to q1] will be correct? 25%

q2=what is the chance [an answer to q1] will be correct?

what is the chance [an answer to q2] will be correct? 50%

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Ashtone
If I choose to answer this question at random (with the constraints of having
to choose one of the choices) then the chance of it being correct is going to
be 25%, because I am answering at RANDOM, therefore not using any intellect
and not applying any sense to the question.

However, the question merely states IF you choose, not that you have to.

Therefore, I am entirely correct by answering either A or D.

Thus it is not unanswerable and is incorrect in stating so.

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LaPingvino
I choose E) 20%

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donohoe
B

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mahmud
B is the new C

<http://i.imgur.com/LZBup.jpg>

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jheriko
i don't get it... maybe i'm being incredibly dense but it looks like it should
be B. this makes the correct answer 25%, so the probability of getting it
right at random is 50% because 2 out of 4 answers are 25% - so the answer is B
= 50%, and indeed the chance of choosing B is 25%

answering the question at random is not the same as answering the question
posed - so the fact that the two answers are not equal shouldn't be a problem.
right?

edit: i hate paradoxes, i'm pretty certain i'm wrong, but i can't put my
finger on precisely why. :)

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paraschopra
I refuse to play silly mind games which make me feel incompetent.

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stcredzero
A good way to discourage learning in fields like mathematics, science, and
programming.

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paraschopra
Most problems in mathematics, science, and programming aren't as silly as this
one.

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ErrantX
A B C D

(as it is not specified that only one must be chosen)

EDIT: the problem is ill defined...

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rontol
Normally it would be 1 out 4 = 25% but if all answer given in the list is
wrong then 0%

The answer is not in the list thus unanswerable?

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JoeAltmaier
If "I" choose the answer, I use a weighted 4-sided die that comes up "B" half
the time. So B is correct.

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clvv
Saw this one before and if that was the source of this, then the answer will
be E) 0% What a nice one!

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RevRal
The answer is. . . A plus D.

(Seriously, if I saw this on a test I'd just circle A and D then write "=
50%".)

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techiferous
My random answer is "splorichoo".

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gurtwo
I say B. Now prove me wrong.

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jey
"You're wrong because the answer key says so. Were you not paying attention
when I gave the answers to use during the 'review' session?"

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jonsen
The answer is C because it's B.

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katovatzschyn
Appears to be a clever case of the first incompleteness theorum.

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tdmackey
Gödel's first incompleteness theorem states that any effectively generated
theory capable of expressing elementary arithmetic cannot be both consistent
and complete. In particular, for any consistent, effectively generated formal
theory that proves certain basic arithmetic truths, there is an arithmetical
statement that is true, but not provable in the theory (Kleene 1967, p. 250)
per <http://en.wikipedia.org/wiki/Gödels_incompleteness_theorems>

Just because you title something an "Unanswerable question" doesn't mean it
actually is, and certainly doesn't mean the first incompleteness theorem is
relevant.

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jaekwon
Is "The above question has no solution", which is choice C, not a Godel
sentence?

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tdmackey
No. Godel's incompleteness theorems say nothing about non-arithmetical or non-
mathematical statements nor do they apply in contexts where no formal system
exists. Some sort of paradox, sure, but Godel doesn't apply.

Truth is not a mathematical concept, and determining the "truth" or
"falsehood" of a sentence has nothing to do with Godel's incompleteness
theorems.

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JoeAltmaier
Boolean logic is an "arithmetic system"

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rontol
B) for me

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pathik
B

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wendroid
Your rubric doesn't denote whether I can answer more than one item for the
question therefore based on "you can only choose one" then 25% is the chance
of being right, as the correct answer is still one of A,B,C,D.

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jjs
0% chance.

Answering randomly may give you a _result_ that coincidentally matches the
truth, but you have provided no logical or epistemological support for your
choice, nor any chain of reasoning that leads you from the available evidence
to a conclusion that there even _is_ a correct answer.

You have a 25% chance of randomly choosing the "right" answer, _(C) 0%_ , but
no paradox is created because you answered without establishing knowledge of
the answer, and therefore your answer cannot rightly be called _correct._

