I just saw this online:
If you choose an answer to this question at random, what is the chance that you will be correct?
A. 25%
B. 0%
C. 50%
D. 25%
Are you picking a letter or a number?
You pick a letter.
Cute. The nice thing is you can reason it out without much knowledge of probability.
I don’t think it can be answered when the question is worded that way, assuming I can pick only one answer and have to choose one.
If 25% were the correct answer, both A and D would meet the criteria, which would be selected 50% of the time at random, thus nullifying A and D as correct possibilities. Now one might think C is the answer, as that is also 50%, but if it were, it would only be selected at random 25% of the time, thus nullifying itself as well. If the answer were 0%, then B would be correct, except the fact that B is correct means it can no longer be true, as it will be selected 25% of the time.
I don’t think this is a probabilities question, looking at it this way, but I might have missed something.
Going a step beyond this, what if the correct answer is 10%? That’s not even a choice. So you have no chance of picking the correct answer if you chose an answer at random.
But if you have 0% chance of getting the correct answer at random, then you have a 25% chance of choosing B, which is the correct answer, at random.
I will state right now that I have presented the entire problem as I saw it. I don’t know what the correct answer is. I also don’t know if there is a correct answer or if this is just a trick question with no answer.
0%. A number I picked randomly.
It’s a paradox, if it helps. So, yes, a trick question of sorts.
ETA: 0% is definitely not it. If the true probability of getting the correct answer is 0% but the probability of choosing the 0% option is 25%, then clearly, that can’t be it.
One could just as well ask a similar question, with the answer choices
A: 1/2
B: 1/3
C: 1/2
D: 1/6
E: 1/2
F: 1/3
Now, instead of none of the answers working, any of them works.
Yes, this. As @DMC explained, you have a 50% chance of answering “25%” and a 25% chance of answering “50%” and a 25% chance of answering “0%” (as I belive the question was meant to be interpreted), so no answer is correct.
Not so, because then the actual answer should be 100%. Oh wait.
Absolutely a paradox. Both this and the original.
No, my example wouldn’t be 100%, because that would require all answer choices to be correct at the same time.
On the other hand, I’m still not convinced that any of this is particularly interesting. One could also have a multiple choice question that went
What’s 1+1?
A) 7
B) 3
C) 0
D) cucumber
None of those answers works, either, but nobody says that that’s a paradox. We just say that it’s a bad question.
Or, for an analogue to my six-option question, we could have
What is the correct answer to this question?
A) A
B) B
C) C
D) D
Or for that matter,
What is the correct answer to this question?
A) B
B) C
C) D
D) A
All any of this shows is “it’s possible to use the English language to construct stupid questions”.
No, I don’t feel this is the same thing. In these questions, there is no path to a correct answer. The determination of what a correct answer is doesn’t exist.
But asking what is the probability that a question will be answered correctly is a legitimate question that can produce an objective answer.
For example, if the question was
If you were asked to spell the following words - cat, dog, mouse, pterodactyl - what percentage of them would you spell correctly?
A. 0%
B. 25%
C. 50%
D. 75%
E. 100%
I don’t think anyone would dispute that this question produces a objectively correct answer.
And by extension, if you were asked the following question:
If you chose a random answer to how many of the following words - cat, dog, mouse, pterodactyl - you could spell correctly, what is the chance you would get the correct answer?
A. 0%
B. 25%
C. 50%
D. 100%
Now, let’s say you are an expert speller and you know you can spell 100% of those words. Which is one of the possible answers on the list. So if you randomly chose from the four possible answers, the probability you would choose the correct answer is 25%. B is the correct answer to this problem.
The issue is that this question (what are the chances you will get the right answer) is asking about the answer to a different question (how many of these words can you spell). So I’m not sure if it works if the question is self-reflective like the one in the OP is.
It does seem possible to construct a valid self-reflective question. Like this:
If you choose an answer to this question at random, what is the chance that you will be correct?
A. 100%
B. 100%
C. 100%
D. 100%
Or even:
If you choose an answer to this question at random, what is the chance that you will be correct?
A. 0%
B. 25%
C. 50%
D. 100%
But is that actually valid? I could also say that the correct answer is 0%, as supported by the fact that 0% isn’t one of the answer choices, so you can’t select it.
One problem with self-referential questions like this is that we don’t have a good notion of what “correct” means. And if we try to replace the notion of “correct” with some other notion whose meaning we do know, such as “provable”, then the question becomes fundamentally different.
I would. Sort of. This one not a question in the sense of “this has a correct answer that you should try to deduce or already know”, it’s a question asking you to predict an outcome. If I answer D and then never try to spell those words, did I give the correct answer? Would the others have been incorrect?
This is basically a reformulation of Russel’s Paradox, which asks “Does the set of sets that do not contain themselves contain itself”. If it does, then it doesn’t, and vice versa. A logical paradox.
Self referential questions sometimes have a logically consistent answer, and sometimes they don’t.
I disagree. The question isn’t asking how many of those words you will spell correctly. It’s asking how many you could spell correctly.