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j_sum1
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Truly evil multiple choice question
If you choose a random answer to this question, what is the chance that you would be correct?
A. 25%
B. 50%
C. 0%
D. 25%
I do have an answer to this question but I thought I would let it sit here for a few days of provocation before I give my thoughts.
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Metacelsus
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This is my take on it:
Assuming "choose a random answer" means "choose an answer listed below from A-D", this is a paradox.
If the actual answer is A, then there is a 50% chance of choosing the correct answer, since D is also 25%.
If the actual answer is B, then there is a 25% chance of choosing the correct answer.
If the actual answer is C, then there is a 25% chance of choosing the correct answer.
If the actual answer is D, then there is a 50% chance of choosing the correct answer, since A is also 25%.
None of these probabilities match with their listed chances. Therefore, none of the answers are correct.
Also, this seems more like a Whimsy topic.
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Magpie
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I have forgotten the math behind this but I will guess 1/3.
The single most important condition for a successful synthesis is good mixing - Nicodem
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Texium
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I've come to the same conclusion as Metacelsus. I look forward to having my mind blown.
I think this thread can stay here in Miscellaneous at least until the answer is given so more people have a chance to ponder it.
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diddi
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you are all looking at the value of the answer, not the answer "A","B", "C", "D"
if you think the value of the answer is "25%" and answer "A" but the correct answer is "D" then you would be incorrect.
there is a 1 in 4 chance of selecting the correct letter corresponding to the letter on the answer sheet
so my answer is 0.25
Beginning construction of periodic table display
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phlogiston
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It lacks a definition of correct.
If one assumes that either 0%, 25% or 50% is a correct answer, then
if the answer is 0% you have a 25% of guessing correctly
if the answer is 25% you have a 50% of guessing correctly
if the answer is 50% you have a 25% of guessing correctly
If however the answer is "A" (or "B", "C" or "D"), then there is a 25% possibility of guessing it.
If, however, the correct answer is "elephant", then it is highly unlikely that you randomly answer that but not 0% (as evidenced by the fact that I
just did).
-----
"If a rocket goes up, who cares where it comes down, that's not my concern said Wernher von Braun" - Tom Lehrer |
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Sulaiman
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If you choose a random answer to this question,
what is the chance that you would be correct?
Answer : C = 0%
because RANDOM answers to this question include 3.14156, bannana, 1xRty4c ......
.i.e. there are an infinite number of RANDOM answers, the chance of being correct is zero.
CAUTION : Hobby Chemist, not Professional or even Amateur
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wg48
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Assuming the obvious meaning
A and D (25%) must be incorrect because the chance you will pick them is 50%.
B 50% must be incorrect becuse the chance you will pick it is 25%
C 0% must be incorrect because the chance you will pick it is 25%
So none of the answers are correct but that would make C correct ???
It a variation on the "this statement is a lie" problem
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j_sum1
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All doing well so far. At least one person has given what I would consider close to a correct answer but no one has fully explored the logic behind
it.
[Edited on 7-9-2016 by j_sum1]
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woelen
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This is not a logical thing, but a play with language. It is of the same type as the following:
Can an omnipotent allmighty god make a stone which is so heavy that he cannot carry it along?
This sentence does play with language and does not tell anything about logic, nor about theology, nor about mathematical/boolean reasoning. We can
contrive linguistic constructs which are inherently nonsensical.
I think that the multiple choice question of this thread belongs to the same class of constructs.
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j_sum1
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Not entirely woelen. Language does come into it but there are some hidden assumptions as well. It is possible to make some progress towards a
probable solution, and that using logical deductive reasoning. It is not of the same ilk as statements like, "This sentence is a lie".
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Eddygp
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37.5%
Sum 50%, 25%, 25%, 50% and when you divide by 4, you get the expected value (which in this case is a probability).
[Edited on 7-9-2016 by Eddygp]
there may be bugs in gfind
[ˌɛdidʒiˈpiː] IPA pronunciation for my Username |
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woelen
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Quote: Originally posted by j_sum1  | | Not entirely woelen. Language does come into it but there are some hidden assumptions as well. It is possible to make some progress towards a
probable solution, and that using logical deductive reasoning. It is not of the same ilk as statements like, "This sentence is a lie".
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For me, it still remains a matter of language. The answer to this question is indeterminate (which is not the same as 0%).
Of course, I can think of a few hidden assumptions, but I am inclined to think that these are details, which are not really important for the nature
of this question.
One of the assumptions, I see every one using here, is that with four answers, the chance of hitting one specific answer at random is 25%. This need
not be true, there could be a non-uniform distribution, e.g. 10%, 10%, 40%, 40%. But whatever distribution you choose, the answer still remains
indeterminate.
Another thing which is unclear is what is "correct". Someone else in this thread already stated that the concept of "correctness" must be explained
precisely in this context. Is there one correct answer, or are there more correct answers?
So, I have the feeling that it is a matter of language, but most likely it is more subtle than the "this statement is not true" type of thing. Maybe
it also has to do with "pulling yourself up on your own hair"? I'm not sure about that, I need to think things over a little more.
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j_sum1
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@woelen
[edit]
I have just typed up my answer which I will post on the weekend. You will see why I am smiling when you read it.
[Edited on 7-9-2016 by j_sum1]
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CuReUS
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apparently this is a well known question and has been discussed before - https://www.quora.com/If-you-choose-an-answer-to-this-questi...
the explanation by brady postma ( 2nd answer) seems to be the most logical
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woelen
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I do not agree with the answer in the quora thread. The intent of the author is taken into account and Brady in fact dismisses the question. If we
have to add that kind of arguments, then indeed we'd better just as well stop this entire discussion, but I think that this is a too easy way of
getting rid of the problem. It does not demonstrate the willingness to truly think over this interesting problem.
I am looking forward to j_sum1's answer!
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Magpie
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Without much effort I think I can refine my answer to:
>1/3 but <1/2
Now I will consult my freshman math book to see if I can further refine my answer. 
The single most important condition for a successful synthesis is good mixing - Nicodem
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Hegi
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| Quote: Originally posted by Magpie | Without much effort I think I can refine my answer to:
>1/3 but <1/2
Now I will consult my freshman math book to see if I can further refine my answer. |
Go for it. I also think the answer is in this interval.
Our webpage has been shut down forever cause nobody was willing to contribute. Shame on you all!!!
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aga
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There are no mathematical boundaries : it must be a linguistics problem.
The A,B,C,D values are red herrings, i.e. not part of the Question.
The question is fundamentally 'what is the chance of answering no specific question correctly ?'
I'll go for 0% as that's as close to 1/infinity as the available Answer options offer.
Edit:
Crap.
I don't have an infinite number of answers in my head, and the question would likely be asked by another Human, so likely i'd know at least some of
what they know, so that'd make it significantly More likely that i could guess a correct answer.
Probably something to do with Money, Sex, Work or Other People, so more like 25%.
[Edited on 7-9-2016 by aga]
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careysub
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I think Woelen's first comment is on the money, that this is just a language game.
The "question":
"If you choose a random answer to this question, what is the chance that you would be correct?"
is not really a question at all, although it has the grammatical form of one.
It is exactly in the same class as any other implicitly self-referential language construct which has no truth value.
To bring the point home, what is "this question"? What is it asking?
The answer is nothing, it implies there is a question present, yet none is stated. The second phrase "what is the chance that you would be correct"
should receive the response "about what?", no question was actually posed.
But what about those multiple choice looking things under the "question"?
Yes, what about them? They aren't referenced by the "question" and so are irrelevant to it.
If I had printed the same question above, say, and enumerated list of all mammal species, or the verses of the Bible, or the text of the U.S.
Constitution, would you conclude they were an answer to the "question"? Irrelevant things are irrelevant.
If, as jsum_1 asserts, "there are some hidden assumptions as well" then he is tipping his hand that he (or rather the question) is cheating, and the
"answer" that will be claimed depends on a problem definition that was not disclosed but will be assumed by the answerer as part of the answer.
Different assumptions would give different answers, so there is no answer to the problem as presented.
NB: I could argue that a couple of answers are equally acceptable. I favor either 100% - in the sense that any answer to a vacuous statement is true
in logic (vacuous truth), or else agreeing with phlogiston that it is "elephant" - since any answer at all is valid.
[Edited on 7-9-2016 by careysub]
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careysub
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| Quote: Originally posted by aga |
There are no mathematical boundaries : it must be a linguistics problem.
The A,B,C,D values are red herrings, i.e. not part of the Question.
...
[Edited on 7-9-2016 by aga] |
Ooh.. you beat me to it on this crucial observation, while I was typing my answer above.
You are right.
They are red herrings, and if it is claimed that they are not, it is simply because the whole problem was not clearly stated. We can't answer a
problem we are not correctly told.
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aga
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Sorry ! Bad timing on my part, seeing as you typed it out more thoroughly.
[Edited on 7-9-2016 by aga]
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j_sum1
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Self-referential is not the same as self-contradictory. I could post a similar question where there were five options:
A. 0%
B. 20%
C. 40%
D. 60%
E. 80%
This is no less self-referential but does not obviously form a paradoxical situation. If I had posted this one it would not appear as intriguing a
problem and would provoke little discussion. And yet, it would contain the same exact assumptions and inherent problems as the question I have
actually posted. It is the cracking of those issues that I am interested in.
So, more than just linguistics. No red herrings. Some real deduction is required.
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careysub
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| Quote: Originally posted by j_sum1 | Self-referential is not the same as self-contradictory. I could post a similar question where there were five options:
A. 0%
B. 20%
C. 40%
D. 60%
E. 80%
This is no less self-referential but does not obviously form a paradoxical situation. If I had posted this one it would not appear as intriguing a
problem and would provoke little discussion. And yet, it would contain the same exact assumptions and inherent problems as the question I have
actually posted. It is the cracking of those issues that I am interested in.
So, more than just linguistics. No red herrings. Some real deduction is required. |
So tell us what those assumptions are. If doing so "gives it away" then you are only confirming my point.
And I did not say it was a "paradox", I said it had no truth value - i.e. it is meaningless. Many paradoxes have this property, but it is not limited
to them. I don't think it is a paradox, with or without the original list of items or the new ones.
And I argue that changing the unreferenced "multiple choice" items doesn't change the 'question', or its answer, at all.
BTW: My favorite paradox is Newcomb's Paradox -
https://en.wikipedia.org/wiki/Newcomb%27s_paradox
[Edited on 7-9-2016 by careysub]
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aga
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Gah !
The Question, containing a reference to itself, is :
"If you choose a random answer to this question, what is the chance that you would be correct?"
The possible Answers are :
"A. 25%, B. 50%, C. 0%, D. 25%"
Logically, those answers form no part of the Question, yet they are the limited possible answers to the Question, so Do form part of the
question/equation !
I need to drink more on this one.
[Edited on 7-9-2016 by aga]
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