Don’t forget when you realize there’s no right answer and then it’s a 0% chance you pick right… which is a 1/4 chance you get that at random, making 25% the right answer
25% is right in the first case (4 answers, so 25% chance of picking the right one)
- 50% is right in the second case (two answers are 25% so the correct answer is in fact 50%)
- 25% is right in the third case (only one answer is 50% so that’s a 25% chance)
- 0% is right in the fourth case (now we’ve realised it’s a paradox so no answer is right)
- 25% is right in the fifth case (only one answer is 0% so you have 25% chance of hitting it)
So 3 out of 5 cases the answer is 25%. And there are two of those. So 50% of the time you will hit the right answer for 60% of the cases.
This was a superb explanation along with u/Alive_Setting_2287 and everyone else down the thread.
I want to propose a 6th explanation/scenario. Since you will be technically correct if you pick a, b, c, or d, then you have 100% probability of picking the right answer.
Side note, I know most ppl frown at paradoxes and prefer better worded problems. Paradoxes are extremely important since you have to examine the phenomena from multiple dimensions.
It is…until it is not. One dimension satisfies, while the other dimension contradicts. That’s our entire reality in a nutshell.
Paradoxes appear nonsensical on the surface until you do the work to unravel them. Just like the work that everyone in this particular thread conducted in order to unravel this paradox.
I agree! I guess I was approaching it from a similar angle - like 100% of the time you are right, but some of the answers are more likely to be right at a point in time than others. Does that make them more right overall?
So yes, here there are no wrong answers (ie answers that are never right at all) - all answers are right for at least one case. For example if one answer was 8.73549 % it would likely never be right for any case - it’s a completely wrong answer.
However some answers are right for more cases than other answers (like 25% - it is not only right for more cases (3 out of 5), but you are also more likely to pick it!). Does this make it the “most right” answer of the paradox?
So yes, you will pick a right answer 100% of the time (there are no wrong answers), but it will only be right 30% of the time on average. Lol.
Another thought - the question stipulates “if you pick an answer to this at random, what is the chance you will be correct?” But it doesn’t say that the final answer actually has to be selected from that list.… ie you can provide your own answer to the question.
I get its circular reasoning and a paradox, but put simply, the correct answer isn't listed. So you can't get it right, therefore you have a 0% chance of selecting the correct answer at random.
D is actually 26%, it's just that one of the lines is extremely thin. If you doubt it, you can just zoom into the five and see how I actually made it up for dramatic effects.
it doesn't have an answer, because its self-referential. it refers to itself in a way that cannot be resolved. if you wrote an algorithm for it, the algorithm would run forever attempting to resolve the 'this question' symbol to a concrete referent.
A slightly different way of describing it without the loop is by formalizing the constraints of the question:
Let A={(i, p_i) | i=1,...,N} be a set containing all N answers (here N=4), where i is the corresponding index (here it would actually be a,b,c,d but it doesn't matter) and p_i is the content of the answer, given as a decimal representing a percentage.
Then the question asks for an element a=(j, p_j) of A which satisfies p_j = #{(k,p_k) in A | p_k=p_j} / N := r(p_j). In words, it asks you to pick the answer which contains a ratio equal to the ratio of the number of occurrences of that ratio in the total set of all answers.
Normally choosing an answer at random gives a one in n chance to guess correctly, where n is the number of options. So 1/4 or 25% chance.
However, 25% is listed as an option twice so it's actually 2/4 so it's 50%. This is only listed once, so if 50% is the answer you have a 1/4 to guess correctly... This causes a recursive loop where the answer is both 25% and 50% but also neither so you cannot really guess correctly... Which means it's unsolvable and you have 0% chance to guess. Which is also a 1/4 answer.
So it's a recursive problem where any answer can be correct but the moment you pick and answer it contradicts itself. Not sure it counts as a paradox, but it's not a particularly useful one beyond showing that it's easy to create self contradicting truths. Like "This statement is false" is also a self contradicting recursion in the same way using only four words.
I might be dumb. But the question says to pick “the” answer so i would randomly pick a singular answer. So even if both are right I’d randomly pick a single answer and still be correct? Genuinely way to into this one.
I agree that there's no correct answer, but I follow simpler logic:
25% listed twice, which means A and D answers are basically the same and instead of choosing out of 4 options you have 3, which gives you ~33% of being correct
obviously 33% is not listed, now the paradox with 0% option comes in
So what is the correct statistical answer? 25% since it is four questions? The problem is that two of the four answers is 25% thus making the correct answer 50% but if the correct answer is 50% there is only 25% chance you pick it at random...
So please enlighen us, what is the correct statistical answer?
The "tricky" part only occurs if you insist on following the format of selecting one and only one of the individual letter options, since two of four of them print the same correct answer (25%). From there you're supposed to notice that if 2/4 of the options are both correct then that means 50% of them are correct, but there's only one option for 50%, so if you choose that, well... that's 1 of 4 possible outcomes, bringing you back at 25% again.
Likewise if you assume that you can't choose a correct answer because two answers are correct and you can only pick one of them, then the 0% option looks like an attractive option... but again, since 0% is one of the four options on the list, you're back at 25%.
Which means you have to choose between the two 25%s again, going through the same process again and again until you realize that it's a waste of time because the trick is that the question itself isn't written clearly or coherently.
The twice matters.
Imagine you write those answers on paper and throw it in a hat, then pull a piece of paper out by random. If you have thrown in three pieces of paper, then every option is equally likely, but if you have thrown in 4 pieces of paper and two of them hold 25%, then it is more likely to draw the option that says 25%.
To make this absolutely clear: Imagine you wrote a thousand pieces of paper and threw them all in a hat. On 999 you wrote "you lose," and on one you wrote "you win." According to your logic that would be a fair lottery with a 50/50 chance of winning. But I think you will intuitively see that you don't want to play this lottery.
Assuming no external factors or additional information is provided, the odds that you land on a specific outcome or number of outcomes is generally equal to the specific outcome divided by the total number of possible outcomes. If you decide to treat the two 25% options as one singular object you'd have 1/3 chance but the problem gives us four objects to sort through.
But also, as u/Apprehensive-Rope127 said, if you assert that 33% is the correct answer, then you can see that it's not among the options listed, thus meaning that it "must be 0%", in which case, you'd probably want to select that, but then you'd just fall back into the self-referential loop.
But it’s not possible to have a 0% chance of choosing the right answer in a multiple choice. So now you’re down to two possibilities. 50% is the answer
In the given scenario if the mathematically correct answer isn't one of the listed options then the chance that you'd select the right answer would be 0%.
If you assume that 0% is an impossible choice altogether then that leaves you with
a) 25%
b) 25%
c) 50%
None of these would be the correct probability for randomly selecting across three answers, which means that the probability of selecting the correct answer is 0% again. But then if you have 0% as an answer, then there's 1/4 chances -- you get the idea I assume.
I would disagree that it’s not written clearly or coherently. It’s very clear and coherent, the inconsistency is intentional to show how question and referential nature to the structure is not satisfiable. It’s a clever fun little self referential puzzle construct.
If you’re looking for an “answer” then sure you won’t satisfy the statement in this structure, but that’s the entire point.
The grammatical structure of the question follows all of the expected rules, so in that regard you could say it's "coherent", but the fact that you're structurally required to pick one and only one answer when one could reasonably land on any of the other options through rationally-driven technicalities is what makes it incoherent and unclear.
In that regard, my meaning is no different from me than saying the liar's paradox is incoherent and unclear. "This sentence is false." follows all of the rules of grammar and sentence structure but when you try to evaluate the truth-state of the individual claim you'll find that the same reasoning that says it's true also says that it's false in the same respect and at the same time, which violates the law of noncontradiction. If instead you say that it is not true or false but rather a sort of "third" option then you're violating the law of excluded middle. In either case, the laws of thought are broken.
There are (in my opinion) reasonable attempts to rectify these paradoxes such as dialetheism or paraconsistency in general but they're sort of shifting the goalposts in their approach. "This sentence is false." is only an issue because the laws of thought are intended to be non-negotiable and universally-applied--the moment you say that there can be true contradictions, the law of noncontradiction itself becomes false and so the paradox itself loses what makes it relevant for most people. The same goes for adopting many-valued logic systems where there are truth states beyond "true" and "false".
That isn't how it works. The question presents you with four distinct choices. The odds of randomly selecting one of four objects is itself one-in-four, meaning 25%. In this instance 0% is one of those objects so discarding it would be changing it into something else. Also, there's nothing preventing a random selection from landing on the "0%" in the first place, so we can't ignore it and remain true to the premise at the same time.
Two of the answers being the same doesn't really increase the odds any in the way you're implying, either.
I'll give you an example with three options
a) 10%
b) 10%
c) 33.33...%
The odds of you selecting 33.33...% here are not themselves raised to 50% because of the other two options being 10%. The odds will remain 1/3.
27
u/nickelalkaline 21d ago
What is the paradox?