5 ms·
Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ https://blog.floydhub.com/naive-baye
by dtjohnnyb 7y ago
Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ https://blog.floydhub.com/naive-bayes-for-machine-learning/
Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct?
A) 25%
B) 50%
C) 60%
D) 25%
- cyborgx7 7y agoThe answer to that question is obviously 0% Now, what would be the answer to the same question with the answer options: A) 20% B) 40% C) 60% D) 20% E) 0%
- AstralStorm 7y agoYour answer above is incorrect in a very funny way. "At random" implies an uninformed prior, but the question presupposes there's a correct answer, as 0% is missing. 0% and 100% are indefensible for any uninformed prior. There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of ways. It's not a paradox. If it asked the question "knowing that probability of success for random single choice question out of 4 answers is 25%, what is the probability of selecting the correct answer at random from one of the below?" That formulation implies an informed prior. That'd have the answer of prior% with 50% for uniform prior, but it's not duplicated, so the actual answer is 0% making it a paradox. If it were duplicated, (answers only 25% and 50% available) the either answer of 50% would hold. But that was not the question asked in yours or former question.
- cyborgx7 7y ago>0% and 100% are indefensible for any uninformed prior. If none of the answers are correct, the chance of picking the correct answer is 0%.
- AstralStorm 7y agoAgain, not for a question that has a defensible answer present when you're picking at random. (Uninformed prior.) If there is no defensible answer present, it's still not 0%, it's a paradox. The answer is dependent on base axioms accepted. (Axiom of choice and axiom of regularity are a few.) The answer set is Dedekind-finite and countable, whereupon probability is 1/logically consistent answers given the axioms chosen.
- shantly 7y agoWake up, check HN, see a lively argument about whether something that can't happen has a 0% probability of happening or not. Maybe I'll go for a walk.
- cyborgx7 7y agoOf course, a uniform distribution is implied. The fact that you choose to misunderstand this on purpose, doesn't make you smart or right. It makes you a pedant who is still wrong.
- northern-lights 7y agoNot quite. Because the chance is 0%, the fact that you were able to pick the choice (with 0%) at all implies a contradiction.
- Doxin 7y agoAt random has to imply uniform random for the question to make any sense, otherwise you can simply bias your answer choices so the answer is always correct. Given uniform random none of the answers is correct: 25%) There's a 50% chance of choosing this answer 50%) There's a 25% change of choosing this answer 60%) There's a 25% chance of choosing this answer If you're allowed to pick your own random distribution then any answer is equally valid. Say we pick one of the 25% answers 25% of the time, and the other ones uniformly: 25%) There's a 25% chance of picking this, as defined by our random distribution. 50%) 37.5% chance 60%) 37.5% chance But if we instead pick our distribution so we pick the 60% answer 60% of the time and the others uniformly we've suddenly got this answer: 25%) ±27% chance 50%) ±13% chance 60%) 60% chance So depending on if you interpret random as "uniform random" or as "whichever random distribution you like" either none of the answers are right or you can pick any answer to be right.
- olalonde 7y ago> One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of ways. It's not a paradox. Sorry but that seems disingenuous... You are ready to accept that there's a mistake in one of the answers but not that none of the answers are correct?
- TuringTest 7y agoThe right answer is the question: "Is the teacher a Cretan?" :-P
- gatherhunterer 7y agoWhat does it matter if the teacher is from Crete? Being a Cretan does not make one a cretan. You don’t need to be a stoic to realize that.
- vageli 7y agoThis is likely a reference to the Epimenides paradox. https://en.wikipedia.org/wiki/Epimenides_paradox https://en.wikipedia.org/wiki/Epimenides_paradox
- gatherhunterer 7y agoYou’re probably right, but this is not a paradox. There is an answer that is logically sound without conflating the semantics beyond their reasonably-assumed meaning.
- vesinisa 7y agoEven more frustrating would be: Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 20% B) 40% C) 60% D) 20% E) None of the above
- nyhc99 7y agoSo this one is an actual paradox, right? If they would accept both correct answers, then the answer would be 50%, but then if it's 50% those two correct answers would be incorrect.
- cmonnow 7y agoanswer - https://math.stackexchange.com/a/3437700/725808 https://math.stackexchange.com/a/3437700/725808 The question displays a lack of understanding of language, especially the relation between a word and its meaning. More specifically, the relation between a noun and its pronoun. Suppose Question 1 was: > "What day is it today?" And suppose Question 2 was: > "Which answer in this list is the correct answer to this question? > Friday, Saturday, Sunday" If someone asks, 'What question is the pronoun "this" in Question 2 referring to?' Then you can reply - 'Question 1' And then they can proceed to answer Question 2 as 'Saturday' Suppose I just ask you out of the blue : 'what's his height?' You will immediately respond : 'who are you talking about?' A pronoun must come AFTER a noun has been established. If it comes before, the speaker must clarify the noun after. In other words, you must be able to do a Ctrl-H Find & Replace in the original sentence, and change "this" to whatever it's referring to, and the new sentence should still make sense. That is the point of pronouns. If I ask 'what is the weather in this city?' Does that question make sense without mentioning the city's name either before or after? It might make sense grammatically, but practically, it is not answerable. If you now come back and say - Just replace the pronoun "this" with the text of the question, then it becomes : "Which answer in this list is the correct answer to "Which answer in this list is the correct answer to this question" question? Is the question answerable now ? Still NO. Because there is still one unresolved "this". Ad-infinitum. So, to answer your question: > 'which question ?' The question, as is, is not answerable. Because it does not make sense until you resolve what 'this' refers to. Until then, it is just a bunch of words without a corresponding meaning. It's not a paradox or a contradiction. Barber's 'paradox', 'This sentence is false' etc. all are basically just a poor understanding of language/pronouns. You might as well ask : > 'Which answer in this list is the correct answer to oogabooga question?'
- nyhc99 7y agoI think some of your premises are mistaken. >>If I ask 'what is the weather in this city?' >>Does that question make sense without mentioning the city's name either before or after? Yes, it does, if we're standing in a city when the question is asked. "This" would obviously refer to the city we're in. Likewise, in this instance, "this" obviously refers to the question that is currently being asked.
- nothis 7y agoWhat's the correct answer?
- Asooka 7y agoThat depends on whether we consider A and D the same answer or not. If we can assume that A does not imply D and vice-versa, then we can pick either A or D and be correct (but not both) - in essence our picking either answer collapses the question's wave-function to be one or the other.
- Enginerrrd 7y agoI don't think so. A and B are contradictory. A asserts: (A & !B & !C & !D & !E & !F), B asserts (B & !C & !D & !E & !F) which would imply B and !B therefore A is false. Only E (or 5 depending on notation) can be true without contradiction.
- gpsx 7y agoI think the best language to solve this problem is Excel. It says "circular dependency".
- logfromblammo 7y agoAssuming a uniform random distribution: P(A) = 0.25 P(B) = 0.25 P(C) = 0.25 P(D) = 0.25 The possible correct response sets, if multiple correct answers are possible: P({A,D}) + P({B}) + P({C}) = 1 We do know that the answer is only correct if the selected answer is in the set of correct responses: P(x) = P(A & {A,D}) + P(B & {B}) + P(C & {C}) + P(D & {A,D}) P(x|{A,D}) = 0.25 P(x|{B}) = 0.5 P(x|{C}) = 0.6 We can probably assume the response selection and establishing the set of correct responses are independent events, as they are being done by different people, and the person going second has no prior knowledge of the results from the first. P(x) = (P(A)+P(D)) * P({A,D}) + P(B) * P({B}) + P(C) * P({C}) P(x) = 0.5 * P({A,D}) + 0.25 * P({B}) + 0.25 * P({C}) Unraveling: P(x) = 0.25 * P({A,D}) + 0.5 * P({B}) + 0.6 * P({C}) P(x) = P({A,D})/4 + 1/4 P({B}) = 7/2 - 6 * P({A,D}) P({C}) = 5 * P({A,D}) - 5/2 1/2 <= P({A,D}) <= 7/12 0 <= P({B}) <= 1/2 0 <= P({C}) <= 5/12 3/8 <= P(x) <= 19/48 That range doesn't overlap with the possible responses. So there's an incorrect assumption in there somewhere. Maybe the one about the question being fair. Backing up: P({A}) + P({B}) + P({C}) + P({D}) = 1 P(x) = P(A & {A}) + P(B & {B}) + P(C & {C}) + P(D & {D}) P(x|{A}) = 0.25 P(x|{B}) = 0.5 P(x|{C}) = 0.6 P(x|{D}) = 0.25 P(x) = P(A) * P({A}) + P(B) * P({B}) + P(C) * P({C}) + P(D) * P({D}) P(x) = 0.25 * P({A}) + 0.25 * P({B}) + 0.25 * P({C}) + 0.25 * P({D}) P(x) = 0.25 * P({A}) + 0.5 * P({B}) + 0.6 * P({C}) + 0.25 * P({D}) P(x) = 0.25 0 <= P({A}) <= 1 0 <= P({D}) <= 1 P({A}) = 1 - P({D}) So the correct answer is 0.25, and the correct multiple choice response is one of either A or D. One's best response is based on knowledge of the psychology of the test-writer. It is not random. The person writing the question consciously chose one or the other, intentionally violating an assumption of the test-taker--that knowing the correct answer to a question would translate to being able to unambiguously select the correct multiple-choice response.
- kingludite 7y agoNormally 25% but since there are 2 answers with 25% this cant be correct. There is only one answer with 50% but if that is the correct one there would be only 25% chance. Therefore it must be C) 60%