[This replaces my earlier “statistics puzzler” thread wherein I futzed-up the poll choices. I’ve already asked a mod to close that thread]
This is making the rounds on Facebook, and I initially thought I had it pegged until I started reading some of the comments in the article. Now it’s making my brain hurt.
I’m making the question as the poll. Please stand by…
I picked c 40%, but thinking a little more I think e-none of the above is correct.
I voted “none of the above”, but I’d like to change my answer to “Epimenides paradox”.
Don’t know enough to answer.
In a multiple choice question where one of answers must be correct, then the chance of a random selection being correct is, obviously, 100% divided by the number of choices.
But in this case we have not been told, among other things, that one answer must be correct.
In the example, if we assume one of the four answers is correct (20% is listed twice), then the correct answer is none of the above since 25% is not a choice.
I would say “a” and “d” are correct, but it depends on your interpretation of the question. If you interpret the questions as “if you randomly picked answers a, b, c, d, or e, then what is the probability your answer matches up with the answer key answer of a,b,c,d, or e,” then, naturally, the answer is both “a” and “d.” But you are not answering the question at random. You are asked to approach the question as if it were random.
Otherwise, it’s a paradox (and obviously is framed as such), so I don’t think there is a correct answer other than perhaps “e.”
I’m certainly puzzled.
Yeah, I’m not entirely sure I buy my logic on that one. It makes sense to me, but clearly the question is angling for the paradox angle, so I don’t think there could be a correct answer to this question, at least not unless our terms are defined more precisely.
Sta
I think None of the above is wrong because two of the above answers could be right.
What hogarth said.
What the question sets up is a situation where you must choose one state, but it sneakily is asking to satisfy *two *conditions.
One condition is, it must be the probability of a given random chance among 5 equally likely outcomes; that is, 20%.
The second condition is, it must be the probability of getting the correct answer - two out of 5, or 40%.
These conditions are mutually exclusive.
I chose 30%, because fuck it. You’re not telling me how to randomize things!
The question is completely self-referential, it has no connection to anything potentially correct or incorrect. So someone could claim that “none of the above” is the right answer, which, tada! means that there is now a correct answer. But, again the question has no relationship to anything outside of itself, and no answer can really be right or wrong because of that. I still went with None of the Above, because that’s the least specific, least objectionable, answer.
Upthread, Hogarth labeled it “Epimenides paradox” and I’ll trust him on that. The question is similar to a phrase like, “This statement is a lie.” As soon as it becomes right, that makes it wrong. But really it’s never right or wrong to begin with.
Note that the original version of the question didn’t have a “None of the above” choice.
This is correct, and it shows how I messed up on the first thread I started. I added choice e but neglected to adjust the other answers for the 1 in 5 probability. Oh well.
Does the puzzle become solvable if we can’t see what the answers are beforehand? If you envision the “choices” as chits dropped into a bag and one chit blindly chosen (fair enough since the questions says the answer is to be chosen at random), with each chit labeled a, b, c, d on their obverse and 25, 50, 60 and 25% on their reverse. It seems to me that this approach prevents us from languishing over the Epimenides paradox and therefore being unable to confidently select an answer.
So far, 61.54% are voting for (e), so (e) is the correct choice, and the expected chance of being right is about 60%. The question & answers are self-referential, but in this case it does not seem to be leading to a paradox.
Threeve.
Or $Texas.
I haven’t read all the responses, but my thinking was that the “correct” answer is 40%.
If each possible answer were unique and there was only one correct answer, chosen at random, one would have a 20% chance (1 in 5) of choosing “correctly.” (I think there may be a flaw in the idea of choosing “correctly” when choosing at random.)
Imagine 5 differently colored marbles. You choose one at random. How do you know if that color is the correct color? Only by matching some pre-determined “correct” color.
But if two of the marbles are identically colored, does that improve one’s chances, or diminsih them? It’s impossible to tell without having some idea of the pre-determined color. Since that is not the nature of this question, I think it is a red herring.
20% represents a 1 in 5 chance. Since 20% appears twice, one has a 40% chance of picking 20%. That makes 40% the “correct” answer. Since one has only a 20% chance of picking 40%–at random–one has a 20% chance of choosing 40%, and likewise a 20% chance of choosing the correct answer randomly.
Now, what are the odds that I got that right? I suspect I’ve lost just by playing.
I don’t think it has an answer.
If 20% is the right answer then choosing a random option will be right 40% of the time. So (a) and (d) are not right.
If 30% is the right answer then choosing a random option will be right 20% of the time. So (b) is not right.
If 40% is the right answer then choosing a random option will be right 20% of the time. So © is not right.
If “None of the above” is the right answer then choosing a random option will be right 20% of the time. So (e) is not right.
There is no answer which is internally consistent.
I think this question needs rewording in order to be answerable.
“Assuming that there is only one correct answer to this question, and that the one correct answer is one of the choices below, what is the probability of you selecting the correct choice randomly?”
In which case the answer is obviously 20% since there are 5 options and 1 correct response. Not (a) or (d) but 20%. The “answer key” may have been marked with any of them being the “correct” answer, so just ignore whatever the actual choices are and answer with a loud and proud “20%!”