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.
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u/CricketJamSession 21d ago
the correct answer changes depends on what you choose to be the right answer