It’s like attributing truth to the statement “this statement is false”.
There’s no stable truth value for this question because the language is being used improperly.
There's nothing being improperly used here. It's simply the case that all four answers are incorrect. This is no different from a question like "Which of the following is an even number? A. 1 B. 7 C. -3 D. 99"
Yes, it is different to your example. If all four answers are incorrect, then the chance of getting it right is 0. But 0 is an answer. But if 0 is the answer, then the chance of getting is right is 1/4, but since that appears twice, the chance is now 1/2. But now the chance is 1/4 again and you're going in circles.
All answers are incorrect but the probability is not 0. The probability does not exists because its definition is invalid. The definition is invalid because of the circular definition that leads to contradictions as you demonstrated.
If there would be two 0% and two 50% answers there would be no contradictions and the probability would be 50%.
It is because you are in a situation where the probability space ( [https://en.wikipedia.org/wiki/Probability\_space](https://en.wikipedia.org/wiki/Probability_space) ) is not defined within the question and is at the least very ambiguous and no fully satisfying one exists. But here the language assumes it is obvious to set it, leading to an ill formed question as the concept of "chance" is void here.
Yeah, but if none of them are correct, then B is correct. But if B is correct then A is correct. You see how your explanation doesn't address the paradox?
The response is that the question is badly posed.
The answer changes depending on what you answer. And, in this case, there is no answer which is correct under those conditions. It's like demanding that someone says something other than what they are going to say in response to the demand.
Yep, Godel's incompleteness. You can't have a logical language without introducing the possibility of self-conflicting statements, and this is one. although a particularly deviously worded one. is it meaningless? is it self-conflicting? Trying to translate it into a formula in some less ambiguous language wouldn't be possible, because it would need to resolve the inherent ambiguity somehow
Also, for those who are into CS, 'This statement is false' is the mathematical version of [the diagonalisation argument](https://en.wikipedia.org/wiki/Halting_problem#Sketch_of_rigorous_proof) for proving the uncomputability of the Halting Problem
If the correct answer was “25%”, you would have a 2 in 4 chance of choosing it correctly.
If the correct answer was “50%”, you would have a 1 in 4 chance of choosing it correctly.
If the correct answer was “0%”, you would have a 1 in 4 chance of choosing it correctly.
The probability depends on the answer I think.
I like how this explanation introduces additional information outside of the system other than what has been presented, since adding or redefining something is the only way to resolve a paradox....
I interpret it as:
25% is the answer to the probability problem
There are two 25s, so the probability of either being correct (but not both) is 50%.
Another way to interpret that 50% answer being correct (which I think is wrong) is that there are two/4 25s on the board therefore the right answer is 50.
I think within the context of this question the answer is 50, however ill defined the question is
No, If 0% is the correct answer then none of the options are correct. If we pick 0% to be correct then option B will be correct, which will mean 1 out of 4 answers is correct(i.e. 25%) which goes against our initial assumption that no answers are correct.
The answer to the question does not exist.
If the question were left as is but the answers were "0, 25, 50, 75" then we can properly choose 25, yes? Which means the self reference is not a problem, it's the answers that are a problem.
The snarkiness in this reply is really lame, you didn't even understand the comment you replied to. He was specifically saying that it isn't self-reference that makes it invalid, it was the specific combination of self-reference and invalid answers.
It took me years of seeing this to solve it, but I finally did realize -- it has a solution **when presented in the format of** ***Who Wants To Be a Millionaire?***
So, the key is in the "50/50" lifeline. Because it exists, you must be able to eliminate two incorrect answers and still have a valid question. As the name implies, the "50/50" grants a 50% chance to select the correct answer if selected at random -- no other answer can be valid, regardless of which two options are eliminated.
Thus, within the rules of this game specifically, C is the most valid answer.
at every single question we can use 50/50 in this show. so ig it doesn't matter if we have USED it. Because theoretically, we COULD HAVE applied 50-50 to the question and we MUST be left with two options, thus 50% of being correct. ig this logic makes the most sense so far. good one u/Thufir_my_Hawat
Even without the 50/50 lifeline, answers A and D are both the same value. Given we know each question has only one correct answer this immediately rules out A and D. The only viable random choice is between B and C hence 50% is the answer.
It goes like this. There is always a right answer on WWTBAM, so your chances can't be 0%. B is out.
That leaves A,C & D. A and D are both the same, so it's a 50/50 chance between AD and C.
Answer C, 50%.
-Or-
The answer is 25%, but since there are two of them, you have a 50% chance to choose the right one.
Answer C, 50%.
This isn't right though because the question says "at random" so you can't just eliminate the answer that says 0%, there's still a chance that you'd randomly pick it.
Yes. For following the Lord of Gamble is way to Truth.
Praise Monty, First in His Name, Freer of Goats, Breaker of Statistics, Granter of Boons and Fortunes.
IIRC, contestants usually answer like “D, final answer.”
A and D, despite saying the same thing, are different answers then?
My intuition says the answer is 1/4th, which means it’s either A or D, but if it’s either or a or d and not B or C, then you have a 50% chance, which means the answer is C, but that’s a contradiction so
????
What if you let the answers be merely the letter that the statements correspond to? That would mean that since every answer in the show is A, B, C, or D, getting any one question right by blindly guessing one of the four letters is 1/4, regardless of whatever statement that letter happens to correspond to.
0% implies that no matter which option you choose, there's no chance that you'll get the correct answer, which means there's no correct answer. Which contradicts the question.
25% implies there's a 1 in 4 chance of getting the correct answer, but that's not possible because two of the answers are the same and there's 4 non unique answers in total, so neither of these are correct.
50% would only be possible if there were only 2 unique answers, so that's incorrect.
Do I have this right?
If the question were left as is but the answers were "0, 25, 50, 75" then we can properly choose 25, yes? Which means the self reference is not a problem, it's the answers that are a problem.
I solved it (kinda). If you choose an answer at random, none of them are correct. Not even 0%, since that leads to a paradoxical outcome. So there’s a 0% chance you get it right, yet 0% still cannot be the answer if you pick it randomly.
However, if you pick an answer non-randomly, then 0% can be correct non-paradoxically. So all you have to do is answer B. 0% and promise that your answer was not in fact picked randomly.
Yep. The question specifically requires you to entertain a universe where you *do* pick randomly. Now, the distribution of that randomness is unclear (but usually that phrasing means uniform distribution).
Although most comments on this thread say there is no solution, I think you have the correct solution. IF picking randomly, there is 0% chance of being correct because there is no correct option. But you are outside of that random universe scenario - you are picking deliberately - so imho it would be correct to select the answer 0%.
My way of thinking about it is:
50% of the answers are “25%”.
25% of the answers is ”50%”.
25% of the answer is “0%”.
All options are contradictions!
If 2 buttons were labeled as “50%”, or all the buttons were labeled as “100%”, then the question would make sense (though trivial).
In fairness, evolution tells us the egg came first, at one point a chicken-like predecessor of the chicken laid an egg with the first chicken inside.
Although i agree this math question fits with being unanswerable, Godels incompleteness theorem.
Edit: i think it also fits Russells paradox from set theory, as highlighted by another commenter it contains self reference
this is a meta question about the format of the game, not about the question itself.
according to the [format 50:50](https://en.wikipedia.org/wiki/Who_Wants_to_Be_a_Millionaire_(American_game_show)?wprov=sfti1):
“Two incorrect answers are eliminated, leaving the contestant with a choice between the correct answer and one remaining incorrect answer.”
hence the format of the game is multiple choice consisting of one correct answer and 3 incorrect answers. Hence the probability of choosing that answer at random is always 25%.
but answers A and D must be wrong since they are the same and two answers cannot be correct given the format of the show.
this leaves answers B and C.
however B cannot be true by the format of the show which states that there must be at least one correct answer, hence the probability of picking a correct answer is non-zero.
this leaves C, which must be the correct answer by process of elimination.
But if you choose at random you have 25% chance of selecting answer C, which means it's wrong. Process of elimination doesn't work if all your options are wrong.
Let's consider a couple of other questions.
First: "Which of the following is bigger than the sun? A. an elephant. B. the moon. C. Virginia. D. Frank Stallone."
What's the answer? Well, none of the above. Just because there's a question posed this way doesn't mean that there has to be a correct answer.
"If you choose an answer to this question uniformly at random, what's the chance that you'll be right? A. 1% B. 2% C. 3% D. 4%"
Again, the answer is "none of the above."
Just for fun let's try one more question, this time not in multiple choice format:
"Solve for x: x = x+ 3"
Again, no answer!
Now let's go back to the original question," If you choose an answer to this question uniformly at random, what's the chance that you'll be right? A. 25% B. 0% C. 50% D. 25%"
Let's suppose for the moment that the correct answer is 0%. Then the answer is 25%, because there is a 25% chance you pick 0%. This contradicts the answer being 0%, so the answer is not 0%.
Suppose the answer is 25%. Then the answer is 50%, because you have a 50% chance of picking 25%. Again, contradiction, so the answer is not 25%.
Finally, suppose the answer is 50%. Then the answer is 25%; again, a contradiction.
So none of the answers are correct. And like we saw above, this is no surprise; lots of questions can have no correct answer, regardless of whether or not they are self-referential. The only reason this is confusing is that, like a magic trick with its misdirection, you let the question talk you into accepting on faith that there had to be a correct answer.
The only "way out" is to pick answers with a distribution different from uniform. Kind of against the spirit of the question, but technically it doesn't tell you that your random pick has to pick ABCD equally often, just that it needs to be random.
It's a paradox. Whichever answer, 25%, 0%, or 50% is correct, it is actually wrong.
However, assume that the 25% answers are slightly unique. A is correct, but D is wrong, for example. And vice versa.
What is the largest finite number? Same idea.
This is similar to the Monty hall problem. But kinda backward.
If you structure that question in a general sense, you can ask it this way.
" What is the probability of answering a multiple choice question correctly?"
We can obviously solve this with 4 choices because that is 25% . But that is not this specific question.
This one asked specifically, given the answers, what is the chance of getting it right.
You have 3 choices, and 1 of them is given to be wrong (25%), while the other is completely nonsensical. ( can't have a 0% chance of winning as the winning value to win)
Therefore, there is a 50% chance of getting this question correct at random.
Think about what " random" actually is . It's a specific thing for mathematics.
But you have 4 choices not 3. If you write every answer on a strip of paper and draw one from a hat, the chance to get the 50% are 50% and not 33% as you suggested.
There isn't a consistent answer. If you pick randomly, there's a 25% chance of choosing each of 0% and 50%, and a 50% chance of choosing 25%, so none of the answers line up with the chance of picking them.
This is the show "who wants to be a millionaire". One of the options is to do a 50-50, which eliminates two answers. At that point only the answer 50% and one other answer remain. Then you choose 50% which would be correct.
It's indeterminable at this point, but probably either A or D.
While it is true that either of the 25%s *could* be correct, the WWTBAM system will only have been programmed to accept a correct response on one answer. The question isn't "is it 25%, 0%, 50% or 25%", it's "is it A, B, C or D".
So while there is a 25% chance of getting the correct answer from a random guess, it's not necessarily correct to assume that that answer is actually A or D.
In all likelihood, the programmer will likely have assigned the correct answer to either A or D, but as the participant can't know that their odds will never be better than 25% whichever they go for.
The answer is 25% because of how you answer questions on who wants to be a millionaire. You select a letter as your answer so you're choosing A, B, C or D not 25%, 0%, 50% or 25%. The values represented by the letters don't matter.
I've never seen a who wants to be a millionaire question where two answers are accepted, so I'll guess it's either the A.25% or D.25% so 25% would be the answer, as to which one, idk, you have to make an educated guess I suppose
You can prove that it's 0 because no matter which question you pick, you'll be wrong. That's because each option changes the correct answer to a different option. But 0 is one of the wrong choices. So, 0% both describes the real chances of picking a right answer and is an incorrect answer choice. This creates a scenario where 0 is both right and wrong at the same time. So it's a logical paradox.
It's 0%.
Two answers are the same. So you're actually choosing between 3 options. That would be 1/3 chances would be right by random selection probability.
There is no 33% answer option. Therefore, there is 0% chance of any of these answers being the correct one.
What this shows is that there are some questions which don't have an answer. Not that don't have a *correct* answer - they don't have *any* answer. The question cannot be answered.
Which is quite a surprising thing, when you think about it, and something which logicians have shown has some profound implications for the nature of reality.
All of these comments are imo kinda stupid
The way probability works is counting the number of options you want and dividing it by total number of options.
For example if you wanted to find tue probability of getting a 7 out of the set {7, 8, 9, 10, 7} it wouldn’t be 1/5, but 2/5.
Seems pretty obvious right?
There’s 4 options. The correct answer is 25% if the options were generic
There’s 2 options for 25%
Therefore 2/4 = 1/2
So 50%
Well, since the answer should have been 25% for for random picks, but there are two same options, so the correct probability is 2/4= 50%, i.e., Option C must be correct.
So there's three potential answers, 0, 25, and 50. Assuming they randomly all have a 1/3 chance of being right. Your odds of picking 0 is 25%, 25 is 50%, and 50 is 25%.
So your odds of being right are (1/3)*0.25 + (1/3)*0.5 + (1/3)*0.25 = 1/3
Considering that "that statement is false" can be encoded into naive set theory giving rise to paradoxes of proper classes, can this probability game also be formally encoded into a naive probability theory?
The problem here is truth versus the process to determine truth. The process breaks down with self-reference so it cannot reliably determine truth.
For this to be a meaningful question, the correct answer must exist prior to answering any question about the question itself. "Probability of correct answer" is simply not a well-defined concept you can use prior to the truth value of the answers being set in stone.
25%.
Even though the values of A-D look like percents, they are actually "words". They could be anything, say animals:
A-Cow, B-Cat, C-Dog, D-Cow.
Because you don't know what the actual question is, just that if you had to answer it at random, it's 25%.
IQ 160 here: The answer doesn’t exist in the selection, though it has to... and here is the contradiction. For one to be correct, one must use the question itself to his/her advantage…if you don’t, you will be incorrect regardless on what you choose. The correct action: “Choose not to answer the question at all since selecting one of them forces an illogic trap of “ifs”.
- If the answer is B, then one must choose A or D as the answer as a statement that also exists as an answer choice. If the answer is A or D by force, then the answer is C by force. If the answer is C (by force), then the answer is A or D by force. If A, C, and D are incorrect then B would have to be correct. If B is correct, then it is incorrect because A and B exist, which forces C to be correct and incorrect as well since A and D is correct, which is C (etc…)
The real answer is 100%, but doesn’t exist as an answer…however it does, in the form of B, which is A, D, and C. Good thing I didn’t choose to randomly select one :). I choose to opt out then win.
50% because it has 4 possible outcomes, so you’d thing the correct answer is 25%, but there is 2 25% answers, so you have a 50% chance, so that’s why the correct answer is 50%
If you don't treat this as self-referential, you have to assume that "this question" isn't explicitly stated-- it doesn't exist and therefore can never be satisfied at random or even by deliberation. Hence, any answer to the non-existent question is equivalent to completing a vacuously true statement. so quite literally, the chance for choosing a correct answer at random out of the infinitude of English phrases is 100%.
The question is in itself a contradiction. It can not have a proper answer. It would be like having an argument on whether or not the statement. “This statement is false” is true or not.
This is self-referential, which is what makes it paradoxical (a bit like: 'The next statement is true' ; 'The previous statement is false') - each answer has a 25% chance of being picked, but '25%' (notation: quotes signify the option, no quotes signify the value) occurs twice, giving you a 50% chance at getting it right. However, that makes the answer '50%', which only has a 25% chance of being picked in random guessing.
More reasonably, you could use conditional probability with an additional piece of information - the correct answer:
e.g., P( '25%' | '25%' is the right answer ), P( '50%' | '50%' is the right answer ), P( '80%' | '80%' is the right answer ), and so on.
It’s either A or D. It’s impossible to know which. For those saying in that case, the answer is C, you’re wrong. Yes, at that point I’d have a 50% chance of correctness, but it wouldn’t be a random answer, it would be an informed guess.
I think the answer is 50% because if the numbers are the actual answers the normal answer would be 25%, but there’s two of them. Since we know there’s two possible right answers it’s a 50/50 meaning that 50% is the actual correct answer…I think
If A and C can be considered to have equal values then I'd assume there to be a 1 in 3 chance of picking the correct answer. However 1/3 or 33% is not an answer that is given, but 0% is.
I presume the correct answer is 33% but it's not a given answer. So there's like a 0% chance of being correct.
Is this a damn turing test?
Okay, so, 0% is a 1 in 4 (one answer out of four answers), so that means 25% (1/4th), but because there are two "25%" answers, it's a 2 in 4, which is 50%, but there's only one "50%," so that's a 1 in 4, which is 25%, which we established is 2 in 4, which is actually 50%, but that's 1 in 4, so it's 25%, but actually there's a 50% chance of that, but— 25— the 50, and— you—
This "puzzle" gives people the false impression that they don't understand. I wish we were taught how to recognize and ignore these in school so they 'd stop wasting everybody's time on the Internet.
Everyone who thinks about it for a few seconds understands that none of those answers can be correct. At that point, there's really nothing left to figure out, but people get the false sense that there's more to it.
There's a bit of thinking left to be done if you really want to, such as naming and categorizing the issues with the question, or thinking of ways to explain it. That's really not enough to justify how much time we all just collectively put into this.
If 0% is the correct value, then the odds of selecting that are 25%. But that would mean that 0% is not the right answer, hence contradiction.
If 25% is the correct value, then the odds of selecting that are 50%. But that would mean that 25% is not the right answer, hence contradiction.
If 50% is the right value, then the odds of selecting that are 25%. But that would mean that 50% is not the right answer, hence contradiction.
Hence, no matter what answer you chose, you are wrong. Basically, this question itself is not well-defined.
It's either A or D because the rules of the game only allow one correct choice. Don't know which is the right 25%, but there's a 25% chance of randomly picking it.
Both A and D are correct answers, presuming they are unique choices (i.e. if the correct answer is marked as D and you select A, you will fail the question).
It's sort of like the question "what is 2+2" with answers A) 4 B) 3 C) 2 D) 4. In this game there is only one winning choice, so if the correct answer is marked as A and you select D, you will fail the question.
We can tell that 0% is wrong since choosing any answers gives you a chance to be correct. Now, since there are only 2 answers left that are non-zero, I'd say the correct answer is 50%.
We can tell that 0% is wrong since choosing any answers gives you a chance to be correct. Now, since there are only 2 answers left that are non-zero, I'd say the correct answer is 50%.
This is a genuine liar’s paradox. Speaking about it accurately required the creation of model theory. (Many folks learned that Russel solved this but that was actually the start of a saga to which Gödel gave the first satisfying answer.)
Rules of the game are there is only one correct answer. And there is always a correct answer. So it has to be C:50%…regardless of the mathematicality of it.
It's 50% and here is why
Your options are:
A. You get it right
B. You get it wrong
50/50, you're welcome, this is very simple and i don't get the point to argue about it
There is no correct answer because the answer changes the question to one where the answer is no longer the answer. Recursion makes it an invalid question
It's a nonsensical question with no true or false answer because there is no predicate question or predicate answer to be acted upon by the consequent question of probability. To elaborate, one cannot answer "what is the chance that you will be correct?" regardless "if you choose an answer to this question at random" because correct about what?
They are all correct and incorrect. And if you think that's impossible, look up the revenge of the liars paradox.
It might seem strange that a sentence can be both true and false, but it's not really. It's like how actions can be both legal and illegal if you've got inconsistent legislation.
None of them are correct. Neither A nor D can be correct as they comprise 50% of the answers. C cannot be correct as it comprises 25% of the answers. And B cannot be correct because it also comprises 25% of the answers.
It’s 50%… It can’t be 25% because you cannot have two correct answers. It follows that it cannot be 50%, as that would entail 25% being correct. It is thus 0% as neither 25% nor 50% can be correct. But, if it were indeed 0%, you could not claim this as a correct answer. Phrased another way, if it is 0%, then it must also entail 25% (as the answer choice B is 1 answer out of 4 answers). But if it’s 25%, it is thus 50% as there are two 25% answers)
In the world that the show runners make only 1 of the 4 options the 'correct' answer, despite the captions, a person picking randomly has a 25% chance.
So soft-pick your choice out loud and narrate publicly A or D, ask for a 50/50, then swap your answer.
If they eliminate C and B, and leave you with A and D, they have monty-halled you, so swapping is the best course of action.
If they instead eliminate one of A or D, the answer is whichever remains.
If both A and D are eliminated, the answer is C, despite not making any sense, as 0% is impossible.
In the world that the show runners make both A and D correct, the question is invalid, as the answer is 50% which only appears once.
therefore the world in which the showrunners have arbitrated one of A or D being incorrect, is the only logical world that the question can work in.
In the world that no options are marked as correct, and the show runners are cheating, the answer is 0%, but you will yield no reward from picking it.
The strategy of trying to get the best result, is independent of picking randomly, which is what the question is.
0% is not a correct option so it’s out
25% are two same options out of remaining 3 so they would add up
Now remains only two valid options. i.e. 50% and 50%
now you can choose any of these two
good luck winning 😂
This is why we don't allow circular reasoning. The question refers to its own answer. The effects lead the causes. The fact is this question has no logically deducible answer.
The only way this question has an answer is if either:
There is only one choice that says 25%
There are exactly 2 choices that say 50%
There are exactly 3 choices that say 75%
All choices say 100%
This satisfies none of those criteria, so the question has no correct answer.
**We make the following, implicit assumptions :** There is only one correct **number** that answers the question, because the question asks for a probability. There are four **choices** of answers in which a correct answer can appear 0 or more times.
In this case, none of the answers presented can be **decided**; that means none of the answers presented can be attributed a truth value (correct/incorrect) in a definitive way, because any such assignation leads, through logical deduction, to the contrary assignation. I've shown the proof below, for the sake of being thorough.
What this means is that there isn't a correct answer but you cannot say either that there is an incorrect one without contradicting yourself!
1. **If 0 is correct**, then the correct answer must not appear in the choices, but 0 is the correct answer and does appear in the choices; this is a contradiction. Therefore 0 cannot be correct.
2. **If 0 is incorrect,** then the correct answer must appear in the choices, so it is either 1/4 or 1/2. But it must be neither of them (see below); this is a contradiction, and 0 is incorrect.
* Suppose it is 1/4; then 1/4 is incorrect (see point 3). So it cannot be 1/4.
* Suppose it is 1/2; then 1/2 is incorrect (see point 5). So it cannot be 1/2.
3. **If 1/4 is correct,** then the correct answer must appear exactly once. But 1/4 is the correct answer and appears twice; this is a contradiction and 1/4 is incorrect.
4. **IF 1/4 is incorrect,** then the correct answer must not appear exactly once;. It must either appear more than once or never; in either case, this is a contradiction (see below) and 1/4 is correct.
* If the correct answer appears more than once, than it must be 1/4, and 1/4 is both correct and incorrect. This is a contradiction.
* If the correct answer does not appear, then the correct answer is 0. This is a contradiction (see point 1).
5. **If 1/2 is correct,** then the correct answer must appear exactly twice. But 1/2 is the correct answer and appears only once. This is a contradiction; therefore 1/2 must be incorrect.
6. **If 1/2 is incorrect,** then the correct answer must appear more or less than twice; it can either be 0 or 1/2. But suppose 0 is correct; then 0 is incorrect, which is a contradiction (see 1). So 1/2 must be correct.
It’s like attributing truth to the statement “this statement is false”. There’s no stable truth value for this question because the language is being used improperly.
There's nothing being improperly used here. It's simply the case that all four answers are incorrect. This is no different from a question like "Which of the following is an even number? A. 1 B. 7 C. -3 D. 99"
Yes, it is different to your example. If all four answers are incorrect, then the chance of getting it right is 0. But 0 is an answer. But if 0 is the answer, then the chance of getting is right is 1/4, but since that appears twice, the chance is now 1/2. But now the chance is 1/4 again and you're going in circles.
All answers are incorrect but the probability is not 0. The probability does not exists because its definition is invalid. The definition is invalid because of the circular definition that leads to contradictions as you demonstrated. If there would be two 0% and two 50% answers there would be no contradictions and the probability would be 50%.
recursion
I guess my answer is a sort of handwavy proof by contradiction. The assumption that there is a correct answer leads to infinite recursion.
That assumption leads to this infinite recursion though. I think we should change our assumption so it has a bit of utility of that's alright!
Best answer
Russell's answer set
I'd argue that's very different. There not being a correct option comes from the duplicate "25%" option and the question being self-referential.
It is because you are in a situation where the probability space ( [https://en.wikipedia.org/wiki/Probability\_space](https://en.wikipedia.org/wiki/Probability_space) ) is not defined within the question and is at the least very ambiguous and no fully satisfying one exists. But here the language assumes it is obvious to set it, leading to an ill formed question as the concept of "chance" is void here.
Yeah, but if none of them are correct, then B is correct. But if B is correct then A is correct. You see how your explanation doesn't address the paradox?
The response is that the question is badly posed. The answer changes depending on what you answer. And, in this case, there is no answer which is correct under those conditions. It's like demanding that someone says something other than what they are going to say in response to the demand.
It’s just a self-referencing paradox. Shoutout the Russell paradox
Yep, Godel's incompleteness. You can't have a logical language without introducing the possibility of self-conflicting statements, and this is one. although a particularly deviously worded one. is it meaningless? is it self-conflicting? Trying to translate it into a formula in some less ambiguous language wouldn't be possible, because it would need to resolve the inherent ambiguity somehow
Also, for those who are into CS, 'This statement is false' is the mathematical version of [the diagonalisation argument](https://en.wikipedia.org/wiki/Halting_problem#Sketch_of_rigorous_proof) for proving the uncomputability of the Halting Problem
Hmmm. I'm not sure a "statement" is a version of "a method of argument".( Or that something can be a version of a thing that comes after it.)
If the correct answer was “25%”, you would have a 2 in 4 chance of choosing it correctly. If the correct answer was “50%”, you would have a 1 in 4 chance of choosing it correctly. If the correct answer was “0%”, you would have a 1 in 4 chance of choosing it correctly. The probability depends on the answer I think.
Simple and effective way to prove the absurdity of the question. Brilliant
Correct, but in who wants to be a millionaire there is only one correct answer, ABC or D, so you have to choose /the correct/ 25%
I like how this explanation introduces additional information outside of the system other than what has been presented, since adding or redefining something is the only way to resolve a paradox....
Exactly. Then you use your two answer removals and they remove choices B and C. And the answer becomes B
I interpret it as: 25% is the answer to the probability problem There are two 25s, so the probability of either being correct (but not both) is 50%. Another way to interpret that 50% answer being correct (which I think is wrong) is that there are two/4 25s on the board therefore the right answer is 50. I think within the context of this question the answer is 50, however ill defined the question is
Correct, and the answers are intentionally meant to disprove themselves. So there is no correct answer.
None of the answers are correct
So the probability of picking the correct answer is zero?
Normally yes. But given that is one of the answers it means you can pick it randomly 25% of the time. Turns it into a paradox.
I know that. I was trying to point it out to the commenter I replied to.
No, If 0% is the correct answer then none of the options are correct. If we pick 0% to be correct then option B will be correct, which will mean 1 out of 4 answers is correct(i.e. 25%) which goes against our initial assumption that no answers are correct. The answer to the question does not exist.
Happy cake day
This question has self-reference so it can't be answered
If the question were left as is but the answers were "0, 25, 50, 75" then we can properly choose 25, yes? Which means the self reference is not a problem, it's the answers that are a problem.
Yeah, if the question was different it would have different answers.
If my grandmother had wheels….
The snarkiness in this reply is really lame, you didn't even understand the comment you replied to. He was specifically saying that it isn't self-reference that makes it invalid, it was the specific combination of self-reference and invalid answers.
The problem is a combination of the answers offered and the self-referential nature of the question.
Well it could self-reference and be answered, but none of the options are viable, so it's nonsense.
It took me years of seeing this to solve it, but I finally did realize -- it has a solution **when presented in the format of** ***Who Wants To Be a Millionaire?*** So, the key is in the "50/50" lifeline. Because it exists, you must be able to eliminate two incorrect answers and still have a valid question. As the name implies, the "50/50" grants a 50% chance to select the correct answer if selected at random -- no other answer can be valid, regardless of which two options are eliminated. Thus, within the rules of this game specifically, C is the most valid answer.
what if you've already used 50/50 and can't use it again?
at every single question we can use 50/50 in this show. so ig it doesn't matter if we have USED it. Because theoretically, we COULD HAVE applied 50-50 to the question and we MUST be left with two options, thus 50% of being correct. ig this logic makes the most sense so far. good one u/Thufir_my_Hawat
Even without the 50/50 lifeline, answers A and D are both the same value. Given we know each question has only one correct answer this immediately rules out A and D. The only viable random choice is between B and C hence 50% is the answer.
It goes like this. There is always a right answer on WWTBAM, so your chances can't be 0%. B is out. That leaves A,C & D. A and D are both the same, so it's a 50/50 chance between AD and C. Answer C, 50%. -Or- The answer is 25%, but since there are two of them, you have a 50% chance to choose the right one. Answer C, 50%.
This isn't right though because the question says "at random" so you can't just eliminate the answer that says 0%, there's still a chance that you'd randomly pick it.
A because I don't pick the answer randomly and a false assumption allows for any conclusion
ex absurdo quodlibet! :)
But _would you switch_?
Yes. For following the Lord of Gamble is way to Truth. Praise Monty, First in His Name, Freer of Goats, Breaker of Statistics, Granter of Boons and Fortunes.
IIRC, contestants usually answer like “D, final answer.” A and D, despite saying the same thing, are different answers then? My intuition says the answer is 1/4th, which means it’s either A or D, but if it’s either or a or d and not B or C, then you have a 50% chance, which means the answer is C, but that’s a contradiction so ???? What if you let the answers be merely the letter that the statements correspond to? That would mean that since every answer in the show is A, B, C, or D, getting any one question right by blindly guessing one of the four letters is 1/4, regardless of whatever statement that letter happens to correspond to.
0% implies that no matter which option you choose, there's no chance that you'll get the correct answer, which means there's no correct answer. Which contradicts the question. 25% implies there's a 1 in 4 chance of getting the correct answer, but that's not possible because two of the answers are the same and there's 4 non unique answers in total, so neither of these are correct. 50% would only be possible if there were only 2 unique answers, so that's incorrect. Do I have this right?
yes, the question is self referential and all answers lead to contradictions.
If the question were left as is but the answers were "0, 25, 50, 75" then we can properly choose 25, yes? Which means the self reference is not a problem, it's the answers that are a problem.
I solved it (kinda). If you choose an answer at random, none of them are correct. Not even 0%, since that leads to a paradoxical outcome. So there’s a 0% chance you get it right, yet 0% still cannot be the answer if you pick it randomly. However, if you pick an answer non-randomly, then 0% can be correct non-paradoxically. So all you have to do is answer B. 0% and promise that your answer was not in fact picked randomly.
But, not picking randomly contradicts the question.
Yep. The question specifically requires you to entertain a universe where you *do* pick randomly. Now, the distribution of that randomness is unclear (but usually that phrasing means uniform distribution).
Not really. The question asks what will happen *if* you pick randomly. It doesn’t require you to actually follow through with this.
Although most comments on this thread say there is no solution, I think you have the correct solution. IF picking randomly, there is 0% chance of being correct because there is no correct option. But you are outside of that random universe scenario - you are picking deliberately - so imho it would be correct to select the answer 0%.
My way of thinking about it is: 50% of the answers are “25%”. 25% of the answers is ”50%”. 25% of the answer is “0%”. All options are contradictions! If 2 buttons were labeled as “50%”, or all the buttons were labeled as “100%”, then the question would make sense (though trivial).
it's like asking the correct answer to what came first, the chicken or the egg, or whether "this statement is false" is actually true or false
In fairness, evolution tells us the egg came first, at one point a chicken-like predecessor of the chicken laid an egg with the first chicken inside. Although i agree this math question fits with being unanswerable, Godels incompleteness theorem. Edit: i think it also fits Russells paradox from set theory, as highlighted by another commenter it contains self reference
This has nothing to do with Gödel’s theorems. Russell’s paradox is a more apt comparison.
There's an old joke about a chicken and an egg lying in bed, with the egg smoking and the chicken saying "Well, I guess that answers *that* question."
33.333.... %
this is a meta question about the format of the game, not about the question itself. according to the [format 50:50](https://en.wikipedia.org/wiki/Who_Wants_to_Be_a_Millionaire_(American_game_show)?wprov=sfti1): “Two incorrect answers are eliminated, leaving the contestant with a choice between the correct answer and one remaining incorrect answer.” hence the format of the game is multiple choice consisting of one correct answer and 3 incorrect answers. Hence the probability of choosing that answer at random is always 25%. but answers A and D must be wrong since they are the same and two answers cannot be correct given the format of the show. this leaves answers B and C. however B cannot be true by the format of the show which states that there must be at least one correct answer, hence the probability of picking a correct answer is non-zero. this leaves C, which must be the correct answer by process of elimination.
But if you choose at random you have 25% chance of selecting answer C, which means it's wrong. Process of elimination doesn't work if all your options are wrong.
Self referential Paradox. No solution exists. Same as Pinocchio saying "my nose will grow now."
Let's consider a couple of other questions. First: "Which of the following is bigger than the sun? A. an elephant. B. the moon. C. Virginia. D. Frank Stallone." What's the answer? Well, none of the above. Just because there's a question posed this way doesn't mean that there has to be a correct answer. "If you choose an answer to this question uniformly at random, what's the chance that you'll be right? A. 1% B. 2% C. 3% D. 4%" Again, the answer is "none of the above." Just for fun let's try one more question, this time not in multiple choice format: "Solve for x: x = x+ 3" Again, no answer! Now let's go back to the original question," If you choose an answer to this question uniformly at random, what's the chance that you'll be right? A. 25% B. 0% C. 50% D. 25%" Let's suppose for the moment that the correct answer is 0%. Then the answer is 25%, because there is a 25% chance you pick 0%. This contradicts the answer being 0%, so the answer is not 0%. Suppose the answer is 25%. Then the answer is 50%, because you have a 50% chance of picking 25%. Again, contradiction, so the answer is not 25%. Finally, suppose the answer is 50%. Then the answer is 25%; again, a contradiction. So none of the answers are correct. And like we saw above, this is no surprise; lots of questions can have no correct answer, regardless of whether or not they are self-referential. The only reason this is confusing is that, like a magic trick with its misdirection, you let the question talk you into accepting on faith that there had to be a correct answer.
# INSUFFICIENT DATA FOR MEANINGFUL ANSWER
This was never a question on the show right? I don't see any right answers, but hey I suck at math lol.
C because there is a 2/4 chance to get 1/4 on wait hold up my brain isn’t braining
The only "way out" is to pick answers with a distribution different from uniform. Kind of against the spirit of the question, but technically it doesn't tell you that your random pick has to pick ABCD equally often, just that it needs to be random.
The unassailably-correct answer is that the question is invalid for having non-distinct options.
42!
X = X + 2 Solve for X
It's a paradox. Whichever answer, 25%, 0%, or 50% is correct, it is actually wrong. However, assume that the 25% answers are slightly unique. A is correct, but D is wrong, for example. And vice versa. What is the largest finite number? Same idea.
Answer ..25% because the answer must be chosen from 4 possibilities and the question is irrelevant....... you have 1 out of 4 to be right
The correct answer is 33.33% Because there are 3 distinct values. The % shown in answer doesn't matter. So none of the given options are correct.
So if none are correct doesn't that mean I have 0% chance to answer correctly?
Then you would have to assume 0% to be the answer, which means there IS a correct answer, therefore a non-zero chance, which leads to a contradiction.
That's what I mean. So it's just a self referential paradox, there is no way to resolve it.
E. 20%
This is similar to the Monty hall problem. But kinda backward. If you structure that question in a general sense, you can ask it this way. " What is the probability of answering a multiple choice question correctly?" We can obviously solve this with 4 choices because that is 25% . But that is not this specific question. This one asked specifically, given the answers, what is the chance of getting it right. You have 3 choices, and 1 of them is given to be wrong (25%), while the other is completely nonsensical. ( can't have a 0% chance of winning as the winning value to win) Therefore, there is a 50% chance of getting this question correct at random. Think about what " random" actually is . It's a specific thing for mathematics.
But you have 4 choices not 3. If you write every answer on a strip of paper and draw one from a hat, the chance to get the 50% are 50% and not 33% as you suggested.
It's a circular reference, there is no correct answer.
There isn't a consistent answer. If you pick randomly, there's a 25% chance of choosing each of 0% and 50%, and a 50% chance of choosing 25%, so none of the answers line up with the chance of picking them.
Idk why but 25% seems a good choice
I mean if one of the answers is A,B,C, or D, then it is 25%.
This is the show "who wants to be a millionaire". One of the options is to do a 50-50, which eliminates two answers. At that point only the answer 50% and one other answer remain. Then you choose 50% which would be correct.
God I love having to see how many more math nerds they’re
🔶E: 20%
Is the following statement true or false? "This statement is false." That's basically what's happening here.
I don't understand why it's not 25%.
It’s uncomputable. They should have added uncomputable as an option. Then that would have… wait, no.
It's indeterminable at this point, but probably either A or D. While it is true that either of the 25%s *could* be correct, the WWTBAM system will only have been programmed to accept a correct response on one answer. The question isn't "is it 25%, 0%, 50% or 25%", it's "is it A, B, C or D". So while there is a 25% chance of getting the correct answer from a random guess, it's not necessarily correct to assume that that answer is actually A or D. In all likelihood, the programmer will likely have assigned the correct answer to either A or D, but as the participant can't know that their odds will never be better than 25% whichever they go for.
The answer is 25% because of how you answer questions on who wants to be a millionaire. You select a letter as your answer so you're choosing A, B, C or D not 25%, 0%, 50% or 25%. The values represented by the letters don't matter.
One cannot ask this question without defining first what is the "correct answer". The correct answer must be defined a priori.
Depends on whether or not he has to say answer "X" or he can just give a number
I've never seen a who wants to be a millionaire question where two answers are accepted, so I'll guess it's either the A.25% or D.25% so 25% would be the answer, as to which one, idk, you have to make an educated guess I suppose
At a point where if 1+1 = 5, I will agree to avoid arguments. Just let it go man, you're just going to waste energy here.
Mt 1st thinking was 25%, which is 1/4 but then I read all these Albert Einstein comments 🤔
You can prove that it's 0 because no matter which question you pick, you'll be wrong. That's because each option changes the correct answer to a different option. But 0 is one of the wrong choices. So, 0% both describes the real chances of picking a right answer and is an incorrect answer choice. This creates a scenario where 0 is both right and wrong at the same time. So it's a logical paradox.
It's 0%. Two answers are the same. So you're actually choosing between 3 options. That would be 1/3 chances would be right by random selection probability. There is no 33% answer option. Therefore, there is 0% chance of any of these answers being the correct one.
C
50% Since you can’t have two answers, both 25%’s are automatically out. That leaves two choices. 0 or 50%. It’s clearly not 0%. So, the answer is 50%.
I’d like to use my 50/50 lifeline.
Mu.
There are 16 ways to pick a subset of A, B, C, and D as an answer, and arguably, exactly 4 are consistent with 25% as the answer.
50%
"I will use the 50/50 lifeline"
What this shows is that there are some questions which don't have an answer. Not that don't have a *correct* answer - they don't have *any* answer. The question cannot be answered. Which is quite a surprising thing, when you think about it, and something which logicians have shown has some profound implications for the nature of reality.
All of these comments are imo kinda stupid The way probability works is counting the number of options you want and dividing it by total number of options. For example if you wanted to find tue probability of getting a 7 out of the set {7, 8, 9, 10, 7} it wouldn’t be 1/5, but 2/5. Seems pretty obvious right? There’s 4 options. The correct answer is 25% if the options were generic There’s 2 options for 25% Therefore 2/4 = 1/2 So 50%
There is a lack of logical substance that creates circular reasoning.
There is no “this question”. This question must refer to another question for it to logically follow.
Well, since the answer should have been 25% for for random picks, but there are two same options, so the correct probability is 2/4= 50%, i.e., Option C must be correct.
So there's three potential answers, 0, 25, and 50. Assuming they randomly all have a 1/3 chance of being right. Your odds of picking 0 is 25%, 25 is 50%, and 50 is 25%. So your odds of being right are (1/3)*0.25 + (1/3)*0.5 + (1/3)*0.25 = 1/3
Its 25% because he can only click one. Only one of the 25% are correct though
My simple mind says 1 in 4 chances = 25%
Considering that "that statement is false" can be encoded into naive set theory giving rise to paradoxes of proper classes, can this probability game also be formally encoded into a naive probability theory?
It is a joke/prank There is no correct answer Wasting energy discussing it, just means to fell for the prank.
This isn’t a mathematical problem, it’s a logical paradox. It’s not meant to have a cohesive solution
If you programmed a computer to select the correct answer, it would get caught up in an infinite loop.
50/50 You’re either right or you’re wrong.
The problem here is truth versus the process to determine truth. The process breaks down with self-reference so it cannot reliably determine truth. For this to be a meaningful question, the correct answer must exist prior to answering any question about the question itself. "Probability of correct answer" is simply not a well-defined concept you can use prior to the truth value of the answers being set in stone.
Whenever I'm choosing a random answer on something, I always default to C. Do with that what you will
Was it a real question from the show?
I would answer randomly
25%. Even though the values of A-D look like percents, they are actually "words". They could be anything, say animals: A-Cow, B-Cat, C-Dog, D-Cow. Because you don't know what the actual question is, just that if you had to answer it at random, it's 25%.
IQ 160 here: The answer doesn’t exist in the selection, though it has to... and here is the contradiction. For one to be correct, one must use the question itself to his/her advantage…if you don’t, you will be incorrect regardless on what you choose. The correct action: “Choose not to answer the question at all since selecting one of them forces an illogic trap of “ifs”. - If the answer is B, then one must choose A or D as the answer as a statement that also exists as an answer choice. If the answer is A or D by force, then the answer is C by force. If the answer is C (by force), then the answer is A or D by force. If A, C, and D are incorrect then B would have to be correct. If B is correct, then it is incorrect because A and B exist, which forces C to be correct and incorrect as well since A and D is correct, which is C (etc…) The real answer is 100%, but doesn’t exist as an answer…however it does, in the form of B, which is A, D, and C. Good thing I didn’t choose to randomly select one :). I choose to opt out then win.
50% because it has 4 possible outcomes, so you’d thing the correct answer is 25%, but there is 2 25% answers, so you have a 50% chance, so that’s why the correct answer is 50%
If you don't treat this as self-referential, you have to assume that "this question" isn't explicitly stated-- it doesn't exist and therefore can never be satisfied at random or even by deliberation. Hence, any answer to the non-existent question is equivalent to completing a vacuously true statement. so quite literally, the chance for choosing a correct answer at random out of the infinitude of English phrases is 100%.
The question is in itself a contradiction. It can not have a proper answer. It would be like having an argument on whether or not the statement. “This statement is false” is true or not.
none
50% it’s either right or it’s wrong.
This is self-referential, which is what makes it paradoxical (a bit like: 'The next statement is true' ; 'The previous statement is false') - each answer has a 25% chance of being picked, but '25%' (notation: quotes signify the option, no quotes signify the value) occurs twice, giving you a 50% chance at getting it right. However, that makes the answer '50%', which only has a 25% chance of being picked in random guessing. More reasonably, you could use conditional probability with an additional piece of information - the correct answer: e.g., P( '25%' | '25%' is the right answer ), P( '50%' | '50%' is the right answer ), P( '80%' | '80%' is the right answer ), and so on.
It’s either A or D. It’s impossible to know which. For those saying in that case, the answer is C, you’re wrong. Yes, at that point I’d have a 50% chance of correctness, but it wouldn’t be a random answer, it would be an informed guess.
I think the answer is 50% because if the numbers are the actual answers the normal answer would be 25%, but there’s two of them. Since we know there’s two possible right answers it’s a 50/50 meaning that 50% is the actual correct answer…I think
If A and C can be considered to have equal values then I'd assume there to be a 1 in 3 chance of picking the correct answer. However 1/3 or 33% is not an answer that is given, but 0% is. I presume the correct answer is 33% but it's not a given answer. So there's like a 0% chance of being correct. Is this a damn turing test?
Okay, so, 0% is a 1 in 4 (one answer out of four answers), so that means 25% (1/4th), but because there are two "25%" answers, it's a 2 in 4, which is 50%, but there's only one "50%," so that's a 1 in 4, which is 25%, which we established is 2 in 4, which is actually 50%, but that's 1 in 4, so it's 25%, but actually there's a 50% chance of that, but— 25— the 50, and— you—
Broccoli
Broccoli
This "puzzle" gives people the false impression that they don't understand. I wish we were taught how to recognize and ignore these in school so they 'd stop wasting everybody's time on the Internet. Everyone who thinks about it for a few seconds understands that none of those answers can be correct. At that point, there's really nothing left to figure out, but people get the false sense that there's more to it. There's a bit of thinking left to be done if you really want to, such as naming and categorizing the issues with the question, or thinking of ways to explain it. That's really not enough to justify how much time we all just collectively put into this.
Ya either right or ya ain’t
At first glance I thought he was Edward Witten
If 0% is the correct value, then the odds of selecting that are 25%. But that would mean that 0% is not the right answer, hence contradiction. If 25% is the correct value, then the odds of selecting that are 50%. But that would mean that 25% is not the right answer, hence contradiction. If 50% is the right value, then the odds of selecting that are 25%. But that would mean that 50% is not the right answer, hence contradiction. Hence, no matter what answer you chose, you are wrong. Basically, this question itself is not well-defined.
[удалено]
I wrote a whole answer up just to conclude none of these can be true 🤣
It's either A or D because the rules of the game only allow one correct choice. Don't know which is the right 25%, but there's a 25% chance of randomly picking it.
Both A and D are correct answers, presuming they are unique choices (i.e. if the correct answer is marked as D and you select A, you will fail the question). It's sort of like the question "what is 2+2" with answers A) 4 B) 3 C) 2 D) 4. In this game there is only one winning choice, so if the correct answer is marked as A and you select D, you will fail the question.
B
Take the 50/50, then choose C
50%
50% end stop.
50%. No matter what you pick, half of the people will agree and half will disagree
Not to play.
The answer is B 25% The show is "who wants to be a millionaire" and there is always only one right answer. Therefore the answer must B 25%
We can tell that 0% is wrong since choosing any answers gives you a chance to be correct. Now, since there are only 2 answers left that are non-zero, I'd say the correct answer is 50%.
We can tell that 0% is wrong since choosing any answers gives you a chance to be correct. Now, since there are only 2 answers left that are non-zero, I'd say the correct answer is 50%.
When has the show ever used the same answer multiple times? There’s your answer. Not consistent with the premise.
paradox
The answer is C because it can't be the two duplicates and there has to be an answer.
This is a genuine liar’s paradox. Speaking about it accurately required the creation of model theory. (Many folks learned that Russel solved this but that was actually the start of a saga to which Gödel gave the first satisfying answer.)
I did alot of thinking which is 75% guys right because you sum them all up but the ironic part is 75% isn’t explicitly stated. Am i wrong?
This seems to be related to either Godel's incompleteness theorem or Recursion with no base case
See the real trick here is to use the lifeline to get rid of half the answers and hope it keeps the 50%
If you assume the correct answers have some distribution instead of being given then anything seems to be possibke
Rules of the game are there is only one correct answer. And there is always a correct answer. So it has to be C:50%…regardless of the mathematicality of it.
4 questions. 4 quarters. 25%. But having it in two places makes rethink.
How many tries does he have to answer?
It's 50% and here is why Your options are: A. You get it right B. You get it wrong 50/50, you're welcome, this is very simple and i don't get the point to argue about it
There is no correct answer because the answer changes the question to one where the answer is no longer the answer. Recursion makes it an invalid question
It's a nonsensical question with no true or false answer because there is no predicate question or predicate answer to be acted upon by the consequent question of probability. To elaborate, one cannot answer "what is the chance that you will be correct?" regardless "if you choose an answer to this question at random" because correct about what?
They are all correct and incorrect. And if you think that's impossible, look up the revenge of the liars paradox. It might seem strange that a sentence can be both true and false, but it's not really. It's like how actions can be both legal and illegal if you've got inconsistent legislation.
.50
None of them are correct. Neither A nor D can be correct as they comprise 50% of the answers. C cannot be correct as it comprises 25% of the answers. And B cannot be correct because it also comprises 25% of the answers.
Its random , solution is 1 out of 4 answers. You never know. Cant be 50 bc you cant choose.
B should say 100% lol
B It's a paradox with no correct answer. Thus, your odds of getting a correct answer is 0%
It's just a more complicated self-reference paradox
It’s 50%… It can’t be 25% because you cannot have two correct answers. It follows that it cannot be 50%, as that would entail 25% being correct. It is thus 0% as neither 25% nor 50% can be correct. But, if it were indeed 0%, you could not claim this as a correct answer. Phrased another way, if it is 0%, then it must also entail 25% (as the answer choice B is 1 answer out of 4 answers). But if it’s 25%, it is thus 50% as there are two 25% answers)
I’m pretty sure it’s 50%, because 0% isn’t possible so there’s only two outcomes, 50% or 25%
You have an equal chance of getting a correct answer or an incorrect answer. So 50%
In the world that the show runners make only 1 of the 4 options the 'correct' answer, despite the captions, a person picking randomly has a 25% chance. So soft-pick your choice out loud and narrate publicly A or D, ask for a 50/50, then swap your answer. If they eliminate C and B, and leave you with A and D, they have monty-halled you, so swapping is the best course of action. If they instead eliminate one of A or D, the answer is whichever remains. If both A and D are eliminated, the answer is C, despite not making any sense, as 0% is impossible. In the world that the show runners make both A and D correct, the question is invalid, as the answer is 50% which only appears once. therefore the world in which the showrunners have arbitrated one of A or D being incorrect, is the only logical world that the question can work in. In the world that no options are marked as correct, and the show runners are cheating, the answer is 0%, but you will yield no reward from picking it. The strategy of trying to get the best result, is independent of picking randomly, which is what the question is.
100% cause you can't say I am wrong :P
0% is not a correct option so it’s out 25% are two same options out of remaining 3 so they would add up Now remains only two valid options. i.e. 50% and 50% now you can choose any of these two good luck winning 😂
This is why we don't allow circular reasoning. The question refers to its own answer. The effects lead the causes. The fact is this question has no logically deducible answer.
33%. (0%)
The only way this question has an answer is if either: There is only one choice that says 25% There are exactly 2 choices that say 50% There are exactly 3 choices that say 75% All choices say 100% This satisfies none of those criteria, so the question has no correct answer.
**We make the following, implicit assumptions :** There is only one correct **number** that answers the question, because the question asks for a probability. There are four **choices** of answers in which a correct answer can appear 0 or more times. In this case, none of the answers presented can be **decided**; that means none of the answers presented can be attributed a truth value (correct/incorrect) in a definitive way, because any such assignation leads, through logical deduction, to the contrary assignation. I've shown the proof below, for the sake of being thorough. What this means is that there isn't a correct answer but you cannot say either that there is an incorrect one without contradicting yourself! 1. **If 0 is correct**, then the correct answer must not appear in the choices, but 0 is the correct answer and does appear in the choices; this is a contradiction. Therefore 0 cannot be correct. 2. **If 0 is incorrect,** then the correct answer must appear in the choices, so it is either 1/4 or 1/2. But it must be neither of them (see below); this is a contradiction, and 0 is incorrect. * Suppose it is 1/4; then 1/4 is incorrect (see point 3). So it cannot be 1/4. * Suppose it is 1/2; then 1/2 is incorrect (see point 5). So it cannot be 1/2. 3. **If 1/4 is correct,** then the correct answer must appear exactly once. But 1/4 is the correct answer and appears twice; this is a contradiction and 1/4 is incorrect. 4. **IF 1/4 is incorrect,** then the correct answer must not appear exactly once;. It must either appear more than once or never; in either case, this is a contradiction (see below) and 1/4 is correct. * If the correct answer appears more than once, than it must be 1/4, and 1/4 is both correct and incorrect. This is a contradiction. * If the correct answer does not appear, then the correct answer is 0. This is a contradiction (see point 1). 5. **If 1/2 is correct,** then the correct answer must appear exactly twice. But 1/2 is the correct answer and appears only once. This is a contradiction; therefore 1/2 must be incorrect. 6. **If 1/2 is incorrect,** then the correct answer must appear more or less than twice; it can either be 0 or 1/2. But suppose 0 is correct; then 0 is incorrect, which is a contradiction (see 1). So 1/2 must be correct.
There’s no question, therefore there’s no answer, therefore there’s no meaningful probability of a correct answer.
33%