The distinction between being able to answer a question and the ability to analyze a question is precisely why Communist China will never be a superpower -- no matter who "mathy" their education is.
With a random number generator that spews out numbers fom 1-4, or if you put the letters a-d in a hat, then the answer is b. 50%
But if a person is looking at the list and consciously deciding to guess, then there is a 33% chance of being correct, since they will recognize a & d as being the same answer. So technically, there are only 3 answers available to you. But there is no 33% answer, which means their chance of being correct is 0%. And that is not on the list of answers either. So maybe this is a question of philosophy, sort of like "Can God make a stone so big He can't lift it?"
None of the four responses are correct answers, so there is 0% probability of picking a correct answer at random.
A better structured question would replace the C) 60% response with 0%, closing the loop so that every response would invalidate itself. As it stands, response C) 60% contributes nothing.
@Andre: It's an all Cretians are liars problem. Ordinarily, if you selected randomly from among four options, you chance of getting the correct answer is 25%. However, since there are two options that list 25% as the answer, your chance of selecting one is 50%. But then again, if the correct answer is 50%, you have only a one in four chance of selecting it, making the selection probability 25%, ad infinitem.
Since the answer can't be both 50% and 25% simultaneously, the question must be semantically null and convey no meaning.
If you do the test in two stages, then the answer is B. But it's by no means clear from the syntax and the answer options that you are allowed to separate the two steps. If not, the answer is A or D.
Can anyone find a justification for C? I've tried. I could make a case for 75% (which wouldn't convince me, try 100%?) but 60% seems just a bog standard red herring, and I'd hope for better.
Obviously to me at least Andre is correct. However there is really no question to be answered. So given that we must assume one of the answers is correct It seems to me that the answer would be either 50% or as Andre suggests 33%. If we assume that one of the answers has to be correct then the only valid answer is 50%. This is of course assuming that one of the answers has to be correct. A real mind fuck.
Rick - yes I have considered that aspect of it (the "there is no question to be answered"), having read a few other responses. AGN-Dan also makes a valid point, that it becomes an endless flip-flop between two answers, each of which invalidates the previous.
I looked at it not from the viewpoint that the answers exist in a vacuum, but rather that there is a sentient being observing them, and making the evaluation that the list contains 3 answers, not 4.
Is this some sort of existential (is that the right word?) experiment meant to postulate that reality is the creation of the observer?
If the answer is 25%, your chances of getting it are 50%, thus 25% was not the right answer.
If the answer is 50%, your chances of getting that are 25%, thus 50% was not the right answer.
If the answer is 60%, your chances of picking that are 25%, thus 60% was not the right answer.
If the choices are 25,50,60,33 - then the answer is 25%. The problem arises from 25 appearing as A and D.
Neither the question whose answer we are to pick at random, nor a list of possible answers thereto, is given. The question being asked here - "what is the chance that you will be correct?" - is a separate question, which cannot be answered with the data provided.
Intuitively, selecting one item from for randomly gives a chance of 25%. However, that answer exists twice in the list of four items, doubling the chance that "25%" will be selected, so, the odds of correctly choosing the answer, "25%", is 50%, which is happily in the list as option B.
You could give yourself a headache by then considering that "50%" is one of the potential answers, but that's not really answering the question that was asked.
For those that said it should be "60%": that's really only valid with two successive decisions (the Monty Hall problem), and evaluates to 66.6%, not.
Who said A and D were the same "answer". Think scantrons. Personally, I just think someone was being a smartass on the chalkboard, but if you assume the text of the "answers" is irrelevant, the answer is 25%.
If you chose and answer to this question randomly.
What is the chance you will be correct?
Is it multiple choice, or are the a, b, c and d answers actually part of the question? I would say they are part of the question and not to be chosen, you write in the answer 50%.
The problem is that most "true" logic problems are trinary logic problems, not binary logic. Trinary logic allows for three answers, true, false, N/A. The correct answer to this is "N/A" but that's not offered as an option.
The class of not-T/F answers is larger than the other two classes.
1) The probability of randomly selecting a correct answer from a set which contains the correct answer is 0.25 (25%) in cases where there are 4 options.
2) But if 25% is listed twice as an option? Then random selection yields a probability of correctness of 0.50 (50%).
3) But if 50% is correct, the probability of picking the correct answer at random is 25%!
4) But if it's 25% then it's 50%, but if it's 50% then it's 25%.
If yes, then no, if no, then yes. It is what it cannot be.
The paradox comes from the ambiguity in the question: on what is the meaning of 'correct'.
There is a different answer if 'correct' means the correct percentage from if 'correct' means the correct single option designated by a letter A.. D.
Hence the problem could be viewed as linguistic rather than mathematical. Some commenters seem to have recognised this (both on Coyote Blog and the original site), though I don't think anyone has written it quite that way. [But there are too many responses for me to be bothered to check then all.]
There is an assumption being made that "at random" implies that each answer is equally likely to be chosen. But that doesn't necessarily follow. Suppose I choose my answer by rolling a dice and answering as follows:
1 - a
2 - b
3 - b
4 - b
5 - c
6 - d
Then the answer I choose will still be chosen at random. However, now 50% is a consistent correct solution.
Matt:
Ow. Ow ow ow.
My brain hurts now.
October 28, 2011, 8:05 ammorganovich:
that's awesome.
October 28, 2011, 8:17 amJens Fiederer:
Cute. This is NOT a comment.
October 28, 2011, 8:22 amme:
ROTFL! Now, for future reference, please don't make me spew my morning coffe over the keyboard without warning, will you? π This is brilliant.
October 28, 2011, 8:25 amPaul:
The answer is clearly 0%. I think the third answer 60% is meant to be zero. Then it really doesn't have a consistent answer.
October 28, 2011, 8:27 amKipEsquire:
The distinction between being able to answer a question and the ability to analyze a question is precisely why Communist China will never be a superpower -- no matter who "mathy" their education is.
October 28, 2011, 8:29 amjon spencer:
Thought the old rule was, "when in doubt C it out" as C was around a 30% chance of being correct.
October 28, 2011, 8:33 amandre:
With a random number generator that spews out numbers fom 1-4, or if you put the letters a-d in a hat, then the answer is b. 50%
But if a person is looking at the list and consciously deciding to guess, then there is a 33% chance of being correct, since they will recognize a & d as being the same answer. So technically, there are only 3 answers available to you. But there is no 33% answer, which means their chance of being correct is 0%. And that is not on the list of answers either. So maybe this is a question of philosophy, sort of like "Can God make a stone so big He can't lift it?"
October 28, 2011, 8:46 ameddie:
For anyone trying to figure out the right answer, consider this question instead:
"Is the correct answer to this question 'no'?"
... and if that doesn't turn the light on, try this one:
"What is the correct answer to this question?"
Now look at the blackboard above again.
October 28, 2011, 9:25 amCMJDad:
The question is IF you choose. I choose not to answer!
October 28, 2011, 9:43 amTom:
What is the question to be answered?
October 28, 2011, 10:09 amRuss R.:
The answer to the question is easy... 0%.
None of the four responses are correct answers, so there is 0% probability of picking a correct answer at random.
A better structured question would replace the C) 60% response with 0%, closing the loop so that every response would invalidate itself. As it stands, response C) 60% contributes nothing.
October 28, 2011, 10:55 amEscapedWestOfTheBigMuddy:
Write "E) 20%" on the board, then answer the question.
October 28, 2011, 11:35 amAndrew:
This is VERY entertaining. π
October 28, 2011, 11:50 amMark:
@Eddie:
βWhat is the correct answer to this question?β
This is.
October 28, 2011, 12:23 pmAnother guy named Dan:
@Andre: It's an all Cretians are liars problem. Ordinarily, if you selected randomly from among four options, you chance of getting the correct answer is 25%. However, since there are two options that list 25% as the answer, your chance of selecting one is 50%. But then again, if the correct answer is 50%, you have only a one in four chance of selecting it, making the selection probability 25%, ad infinitem.
Since the answer can't be both 50% and 25% simultaneously, the question must be semantically null and convey no meaning.
October 28, 2011, 12:40 pmblokeinfrance:
If you do the test in two stages, then the answer is B. But it's by no means clear from the syntax and the answer options that you are allowed to separate the two steps. If not, the answer is A or D.
October 28, 2011, 2:27 pmCan anyone find a justification for C? I've tried. I could make a case for 75% (which wouldn't convince me, try 100%?) but 60% seems just a bog standard red herring, and I'd hope for better.
Stan:
I agree with Another guy named Dan. You guys who said 0% are stupid.
October 28, 2011, 5:28 pmRick Summerson:
Obviously to me at least Andre is correct. However there is really no question to be answered. So given that we must assume one of the answers is correct It seems to me that the answer would be either 50% or as Andre suggests 33%. If we assume that one of the answers has to be correct then the only valid answer is 50%. This is of course assuming that one of the answers has to be correct. A real mind fuck.
October 28, 2011, 8:21 pmandre:
Rick - yes I have considered that aspect of it (the "there is no question to be answered"), having read a few other responses. AGN-Dan also makes a valid point, that it becomes an endless flip-flop between two answers, each of which invalidates the previous.
I looked at it not from the viewpoint that the answers exist in a vacuum, but rather that there is a sentient being observing them, and making the evaluation that the list contains 3 answers, not 4.
Is this some sort of existential (is that the right word?) experiment meant to postulate that reality is the creation of the observer?
October 29, 2011, 5:13 amjoshv:
If the answer is 25%, your chances of getting it are 50%, thus 25% was not the right answer.
If the answer is 50%, your chances of getting that are 25%, thus 50% was not the right answer.
If the answer is 60%, your chances of picking that are 25%, thus 60% was not the right answer.
If the choices are 25,50,60,33 - then the answer is 25%. The problem arises from 25 appearing as A and D.
October 29, 2011, 6:47 amCapn Rusty:
Neither the question whose answer we are to pick at random, nor a list of possible answers thereto, is given. The question being asked here - "what is the chance that you will be correct?" - is a separate question, which cannot be answered with the data provided.
October 29, 2011, 9:00 amdave:
Intuitively, selecting one item from for randomly gives a chance of 25%. However, that answer exists twice in the list of four items, doubling the chance that "25%" will be selected, so, the odds of correctly choosing the answer, "25%", is 50%, which is happily in the list as option B.
You could give yourself a headache by then considering that "50%" is one of the potential answers, but that's not really answering the question that was asked.
For those that said it should be "60%": that's really only valid with two successive decisions (the Monty Hall problem), and evaluates to 66.6%, not.
October 29, 2011, 10:05 amcaf:
Who said A and D were the same "answer". Think scantrons. Personally, I just think someone was being a smartass on the chalkboard, but if you assume the text of the "answers" is irrelevant, the answer is 25%.
October 29, 2011, 10:59 amCMJDad:
A strange game. The only winning move is not to play. How about a nice game of chess?
October 29, 2011, 11:14 amastonerii:
If you chose and answer to this question randomly.
What is the chance you will be correct?
Is it multiple choice, or are the a, b, c and d answers actually part of the question? I would say they are part of the question and not to be chosen, you write in the answer 50%.
October 29, 2011, 4:36 pmIGotBupkis, Unicorn Fart Entrepreneur:
The problem is that most "true" logic problems are trinary logic problems, not binary logic. Trinary logic allows for three answers, true, false, N/A. The correct answer to this is "N/A" but that's not offered as an option.
The class of not-T/F answers is larger than the other two classes.
October 29, 2011, 9:27 pmIGotBupkis, Unicorn Fart Entrepreneur:
caf: No, it's not. Josh and AGN-Dan explain it right.
October 29, 2011, 9:29 pmRandomReal[]:
Teacher: Bertrand, do you have an answer?
Bertrand: No! I hate math: it's driven me crazy. I'm taking up philosophy.
Teacher: Georg, do you have an answer?
Georg: Don't interrupt me while I am still counting!
Teacher: Kurt, you must have come up with something.
Kurt: Can I add a new axiom?
Teacher: Alan, what does your computer program say?
Alan: It hasn't stopped yet.
Teacher: Douglas, you're the cleverest of the bunch. Do you have an answer?
Douglas: 42
October 30, 2011, 11:59 amLarry Sheldon:
The comments seem to be a classic example of overbraining the question.
October 30, 2011, 3:24 pmKnucklehead:
Russell's Paradox - or a close relative.
1) The probability of randomly selecting a correct answer from a set which contains the correct answer is 0.25 (25%) in cases where there are 4 options.
2) But if 25% is listed twice as an option? Then random selection yields a probability of correctness of 0.50 (50%).
3) But if 50% is correct, the probability of picking the correct answer at random is 25%!
4) But if it's 25% then it's 50%, but if it's 50% then it's 25%.
If yes, then no, if no, then yes. It is what it cannot be.
October 31, 2011, 1:37 pmIGotBupkis, Unicorn Fart Entrepreneur:
>>> If yes, then no, if no, then yes. It is what it cannot be.
No paradox. It's just not a binary logic problem. The correct answer is option 3: "This question is nonsense, given the allowed answers."
November 1, 2011, 8:08 pmHow D. Neighbor:
You've completely ignored the luck factor. Some people are unlucky and will never get the correct answer. So their chance will be 0.
Also the question may be racist. So many math questions are.
(I've eaten WAY too much Halloween candy and am in a smart-aleck mood.)
November 2, 2011, 5:05 amNigel Sedgwick:
The paradox comes from the ambiguity in the question: on what is the meaning of 'correct'.
There is a different answer if 'correct' means the correct percentage from if 'correct' means the correct single option designated by a letter A.. D.
Hence the problem could be viewed as linguistic rather than mathematical. Some commenters seem to have recognised this (both on Coyote Blog and the original site), though I don't think anyone has written it quite that way. [But there are too many responses for me to be bothered to check then all.]
Nice or nasty?
Best regards
November 2, 2011, 5:24 pmperlhaqr:
This is a metaphor for voting, isn't it?
November 2, 2011, 9:08 pmbengrayen:
There are 12 equally possible outcomes. There are 4 correct possible outcomes. Therefore the answer is 4/12 or 1/3 i.e. 33-1/3%
November 4, 2011, 5:16 ambill:
The answer is 1 in 4 which is 25%...since 25% is listed twice the odds are 2 in 4 or 50%.
November 4, 2011, 5:01 pmChris Close:
The possible "answers" if you answer the question randomly are...
"A", "B", "C", or "D"
Random chances of each.
25%
To correct VALUE to the question posed is "25%". The corresponding correct ANSWERS which match the value of the question asked are "A" and "D"
November 5, 2011, 10:16 amEricK:
There is an assumption being made that "at random" implies that each answer is equally likely to be chosen. But that doesn't necessarily follow. Suppose I choose my answer by rolling a dice and answering as follows:
November 5, 2011, 11:02 am1 - a
2 - b
3 - b
4 - b
5 - c
6 - d
Then the answer I choose will still be chosen at random. However, now 50% is a consistent correct solution.
Shelly Rayedeane:
The one who cloned the original loses.
The great deceiver loses.
And that is the most accurate answer.
But what do I know? I'm not the one who has lost all my money gambling on all the wrong things.
November 9, 2011, 11:59 am