3 ms·

The 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 ago
Your 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 ago
    Again, 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 ago
      Wake 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 ago
      Of 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 ago
    Not 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 ago
  At 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?

AstralStorm 7y ago

Your 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 ago
  Again, 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 ago
    Wake 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 ago
    Of 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 ago
  Not 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 ago
At 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?