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careysub
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Quote: Originally posted by aga  | Gah !
Logically, 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. |
Yes, but that is now different from what was originally posed.
And what if it had been formulated as:
"If you choose a random answer to this question, what is the chance that you would be correct?"
The possible Answers are :
"A. 5, B. elephant, C. A, D. your momma"
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j_sum1
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It is framed as a multiple-choice question and so the options given do form part of the question.
In any MC quiz that lacks clarity, it is prudent to determine the "best response". (Which might mean no response at all.)
What I would like to know is where you end up in the logical pursuit of the best response.
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j_sum1
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| Quote: Originally posted by careysub | | 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] |
I haven't come across Newcombe's paradox before. I will take a closer look at that one.
As for revealing the assumptions -- all in good time. Seeing how different people respond to the paradox/contradictions/meaninglessness/absurd (pick
one) is all part of the fun.
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Darkstar
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I guess I'll take a stab at this.
| Quote: Originally posted by j_sum1 | 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 say the answer is C. Something I've noticed is that most people seem to be under the assumption that multiple choice questions can only have one,
single correct answer, which isn't necessarily true. One way we could arrive at the conclusion that there is more than one answer to this question is
through deductive reasoning. If we assume that the answer must be at least one of the four possible choices listed, then there is at least a 25%
chance of choosing the correct answer at random. Given that there exist two choices that could then potentially be correct, we could further argue
that there must also exist a third correct answer:
1. If A and D are both correct answers, then there is a 50% chance of choosing the correct answer at random.
2. If there is a 50% chance of choosing the correct answer at random, then B must also be a correct answer.
3. Therefore, if A and D are both correct answers, then B must also be a correct answer.
But if that were true, we could also go on to make this argument:
1. If A, B and D are all correct answers, then there is a 75% chance of choosing the correct answer at random.
2. If there is a 75% chance of choosing the correct answer at random, then A, B and D cannot be correct answers.
3. Therefore, if A, B and D are all correct answers, then A, B and D cannot be correct answers.
Which brings us to our final argument:
1. If A, B and D cannot be correct answers, then there is a 0% chance of choosing the correct answer at random.
2. If there is a 0% chance of choosing the correct answer at random, then C must be the correct answer.
3. Therefore, if A, B and D cannot be correct answers, then C must be the correct answer.
Thus the only possible choice is C.
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j_sum1
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| Quote: Originally posted by Darkstar |
1. If A and D are both correct answers, then there is a 50% chance of choosing the correct answer at random.
2. If there is a 50% chance of choosing the correct answer at random, then B must also be a correct answer.
3. Therefore, if A and D are both correct answers, then B must also be a correct answer.
But if that were true, we could also go on to make this argument:
1. If A, B and D are all correct answers, then there is a 75% chance of choosing the correct answer at random.
2. If there is a 75% chance of choosing the correct answer at random, then A, B and D cannot be correct answers.
3. Therefore, if A, B and D are all correct answers, then A, B and D cannot be correct answers.
Which brings us to our final argument:
1. If A, B and D cannot be correct answers, then there is a 0% chance of choosing the correct answer at random.
2. If there is a 0% chance of choosing the correct answer at random, then C must be the correct answer.
3. Therefore, if A, B and D cannot be correct answers, then C must be the correct answer.
Thus the only possible choice is C. |
1. There is a 25% chance of selecting C at random.
2. Therefore there is a 25% chance of obtaining the correct answer.
3. Therefore C cannot be the correct answer since it states there is a 0% chance of getting it correct.
4. And so A and D must be the correct answer since they are the answers that state 25%
Go to top of the page and repeat ad infinitum.
Beautiful. Just beautiful. 
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Darkstar
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| Quote: Originally posted by j_sum1 | 1. There is a 25% chance of selecting C at random.
2. Therefore there is a 25% chance of obtaining the correct answer.
3. Therefore C cannot be the correct answer since it states there is a 0% chance of getting it correct.
4. And so A and D must be the correct answer since they are the answers that state 25% |
This occurred to me as well, but I still think it's possible to argue that C is the single best answer out of the four. For starters, I'd argue that
propositions 1-3 above do not imply the 4th. It has already been established that answers A, B and D cannot possibly be correct, so if answer C cannot
be correct either, then there cannot be a 25% chance of choosing the correct answer because there isn't one. Thus there is no reason to then conclude
that the answer must instead be A and D, and thus no reason to start all over again.
Secondly, I'd argue that, because we've already established that answers A, B and D cannot possibly be correct, the conclusion that C is the correct
answer is in fact an unavoidable consequence of the very proposition that it ISN'T. Because if neither A, B, C nor D were correct answers, then the
chance of choosing the correct answer at random would still be 0%. So by showing C to be the wrong answer, you are in fact simultaneously showing it
to be the correct one as well.
And lastly, I'd also argue it is possible to prove that "C is the correct answer" is a true proposition by demonstrating the inconsistency of the
opposite proposition "C is the incorrect answer." According to Clavius's Law, for the sake of consistency, if a proposition (A) is a consequence of
its negation (¬A), then that proposition (A) is true:
(¬A → A) → A
And since the proposition "C is the correct answer" is not only a logical consequence of A, B and D all being incorrect answers, but also C itself
being an incorrect answer, we can then conclude that "C is the correct answer" is a true statement.
Anyway, that's my two cents. This is definitely an interesting question that has got me thinking. I don't necessarily disagree with you, by the way,
just felt like playing a little Devil's advocate is all. 
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aga
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It's definitely a good puzzle.
I asked one of my dogs about it and she sniffed for a second and then went about her normal distal hygiene routines, which is to say, she thought it
was some sort of human crap, but at least edible.
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j_sum1
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| Quote: | 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%
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| Quote: | The answer can best be described as indeterminate.
The difficulty in this problem is that it is self-referential and appears at first observation to be self-contradictory.
However, there are two hidden assumptions contained within the problem. These are worth examining and in doing so there does appear to be a solution
that is to be preferred over others.
The first assumption is that “random selection” implies that each of the four answers may be chosen with equal probability. This is a natural
interpretation of the phrase “choose a random answer”, but not a necessary interpretation. What has to be acknowledged is that whenever a random
selection is required, there must be some kind of random selection process. I might put A, B, C and D on a dart board and use my awesome throwing
skills to make a selection. The selection will be random, that is, subject to chance. But there is nothing to suggest all four outcomes have equal
probability.
I might, with equal validity use a regular six-sided dice and label the faces A, B, B, B, C, D. This would give me a random choice and in this case
the probability of selecting B is 50% which incidentally matches that question option. Thus B could be a correct answer.
Alternatively, I might label an eight-sided dice with A, C, C, C, C, C, C, D. In this case there is a 25% chance of obtaining A or D. Both A and D
state a figure of 25% which matches this probability. Therefore, with this random process, either A or D could be considered the correct solution.
And it would not matter which of the two I chose.
A different six-sided dice could be labelled A, A, B, B, D, D. With this random selection there is 0% probability of obtaining C; which matches
option C. Therefore, C could be a correct answer.
And as it has been pointed out ably by Metacelsus, a perfectly uniform random selection process necessarily leads to a paradox and therefore no
sensible answer at all. There are plenty of random selection processes that lead to such paradoxes: this is not the only one.
(And then there is the reverse paradox. If I select randomly using an eight-sided dice labelled A, B, B, B, B, E, E, D then I could make a case that
all the answers are correct since the probabilities of their selection match the numerical answers provided. This opens up the contradiction that
there is 100% chance of obtaining a correct answer in spite of the fact that 100% is not an option. There is also a second paradox under this scheme
in that contradictory answers should be considered equally true. I find this paradoxical situation even more bizarre than the uniform selection
process.)
Thus we can see that the answer, if it exists is contingent upon the random selection process. Depending on how the examiner defines “random
choice”, any or none of the answers could be considered valid. In other words, it is all in the hands of the examiner. If I am a student answering
this question I am unfortunately not privy to the examiner’s whim on this. The only thing I can conclude is that any of the available options A, B,
C or D could be considered valid by the examiner.
This leads to the second assumption – that there is one and only one option out of A, B, C or D that will be considered correct by the examiner.
And this is the normal assumption in multi-choice questions. It is how they are generally designed. We have, however, already been slammed directly
into a paradox by following natural assumptions. There is no reason to suspect the examiner will play fair. The only thing we know for sure is that
the examiner would consider either zero, one, two, three or four of the available options to be correct – by whatever perverse logic that s/he might
wish to use. I can pretty much ignore the numeric answers at this point and focus on A, B, C and D.
What is interesting here is how quickly different people are to abandon this assumption and state that there are zero correct answers. People seem
less likely to consider two, three or four correct answers.
So, it might be that the examiner considers zero of the answers to be correct. If I knew this for certain it would make answering the question
problematic. There is no way of distinguishing between answering correctly and leaving the question out. For that reason I would shy away from
leaving the answer blank. I could be wrong but it does not look like the intent of the question is to opt out.
It might be that the examiner considers one of the four answers correct. This is the default position. I would not throw out this possibility
without good reason.
It might be that the examiner considers two of the four answers correct. If this was the case then the most likely scenario is that those two answers
are A and D since they are the same. I cannot see any plausible reasoning that would render other combinations to be correct. That is not to say
such reasoning does not exist. Alternatively, the examiner might be being deliberately perverse or have faulty reasoning. But in spite of evidence
of this kind of perversity, I consider these alternatives to be less likely. If two answers are correct then they are probably A and D.
It might be that the examiner considers three answers to be correct. And again it is difficult to see the logic behind that. There might not be any.
In which case there is no real way to choose between the triples available.
It might be that the examiner considers all four answers to be correct. We have already seen that all are possible depending on the random selection
process adopted. If this is the case then it would not matter which one we chose.
Which brings us to the decision of what response to give. Much as I would like to present a series of paragraphs for a complete and justified answer,
it is stated as a multiple choice question which conventionally has me selecting from A, B, C or D. Giving a numerical response such as 25% or some
other number or shouting “elephant” while performing dance would all be responses outside of the scope of the format.
We might consider what would happen if we were actually to circle more than one of A, B, C or D. It is difficult to predict under the circumstances
how such a response might be interpreted. The best clue we have is that the question states choosing a (singular) random answer. On this basis I
would resist the temptation to select more than one option.
If there is one correct answer and I am to choose one, then the best measure I can give for its probability is 25%. This has me choosing either A or
D and I really have no way of preferring one over the other.
If there are two correct answers then, as we have seen, I should feel confident about picking either A or D.
If there are three correct answers then I confess to being bewildered as to the logic behind it. But selecting something is better than nothing and I
am likely to choose one of the three correct options.
If there are four correct answers then it really does not matter which I select – I will be correct.
So, whatever insanity the examiner adheres to, I am well served to choose either A or D as my solution. Either will do but not both.
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I am not pretending that my analysis is the only one possible. Like I said at the start, the answer is indeterminate. But that then raises the
question of how to make good decisions in situations that are ambiguous, probabilistic in nature or where good information is lacking. I think
puzzles such as these are worthwhile brain training for real-life situations.
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Eddygp
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This question is a well known paradox in probability. There is no correct answer and here is the reasoning:
If only one answer was correct, then the probability would be 25% but there are two answers with 25% (A. & D.), so those can't be correct.
If two of the answers are correct, then the probability would be 50% but only one answer is 50% (B.) so that cannot be correct.
The only remaining answer, C. at 0% cannot be correct because then 0 of the 4 answers would be correct and there is only 1 answer of 0%.
So there is no correct answer.
there may be bugs in gfind
[ˌɛdidʒiˈpiː] IPA pronunciation for my Username |
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aga
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Alternatively :-
1. Keep your eye on the Money
3. Trust Nobody, also ignore anyone called 'Nobody'.
1. If it bites, bite it First, and as hard as you can.
7. Do it Big. Do it Once. Do it Alone.
5. Small people can run and hide faster than Big people.
1. Never eat any food that you cannot positively identify.
These also work in real life.
I was going to quote from the bible, but it's a mistranslation.
It should read : "Do unto Udders ..."
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