This is a paradox. Because the answer is 25% because there are 4 options. But, because there are 2 options with 25%, that makes 50% chance. However, there is only one 50% option, so 25% chance of getting it right. But there are two 25% options, and so on...

It's not a paradox. Since none of the listed answers can be considered correct, than chance of getting the question correct by randomly guessing one of them is 0%

Wouldn't it be like this: since there are four options, initial chance is 25%. But, since two options are same, shouldn't the chance go up to 33.33333% instead of 50%.

I don't think it's a paradox, because it's not actually asking you to answer the question randomly, but rather to report what would happen... if you did that a bunch of times.

I was thinking about this one for a while. To get the right answer you have to ignore the answers the teacher supplies on the test. Suppose you have 4 objects in a box labeled A, A, B, C and in a second box you have three objects representing the values of the choices A', B', C'. In box 1, P(A) = .5, P(B) = .25, P(C) = .25 and in the second box P(A') = P(B') = P(C') = 1/3. You have to calculate the individual probabilities that your guess will match the correct answer, and then add them together. So P(Correct) = P(A and A') + P(B and B') = P(C and C') = (1/2)(1/3) + (1/4)(1/3) + (1/4)(1/3) = (1/3) so picking one of the four answers has a 1 in 3 chance of success. I'm going to go ahead and agree with the people further down that the true answer is 0%.

If they add a 100% it would be the correct choice as it would be true if it was the correct answer and it is the only one that would have that behavior. Therefore 100% would be the only correct one by process of elimination.

All of the provided answers are incorrect. The answer cannot be A or D because they comprise 50% of the options; as they say the answer is 25%, that's wrong. The answer cannot be C because C is only 25% of the options and it says the answer is 50%, so it's wrong. B is just a random number that has no bearing on anything.

I would still pick 25 for this reason: the two listed 25s force the answer to be the 50% chance. However in picking 50% the right answer is only still listed once, at a 25% chance of 4 options. So to pick the correct answer (50) is now once again a 25% chance. Where's that two astronaut earth meme when I need it.

EDIT: Another way to think about this is what the probability is for a random number picked from {25,50,60} to match a random number picked from {25,25,50,60}.

I think I solved it. No where in this question does it say you HAVE to pick one of the answer choices for your answer to the question. But it does stipulate that for the random choosing, one of the four answer choices will be chosen. All of the answer choices are wrong, therefore there's a 0% chance to get the answer correct by randomly picking. However, you can still get the question correct by either writing down "0%" or circling a "0%" in either answer choice B or C.

Im propably stupid, but it says randomly. So its like blind choosing. 1 of the 4 must be correct. So if you dont look at the numbers, there is a 25% chance. That means that 1 of the 25% is wrong. We would have to know the exact number of correct answers possible.

There are three answers that you could choose randomly with their respective probability: 25% with 50% probability, 50% with 25% probability, 60% with 25% probability. All of this is wrong.

Picking a or d is correct but you only have a 50% chance of being correct. Because this is a trick question and you can pick a b c or d, you have a 25% chance to guess correctly.

I love that everyone has different answers here! Rare for a tdtm. I’ll submit my own to the pile. Here is my claim: (d) is correct. Not (a),(b), or (c). Only (d) is correct. We can verify my claim by checking the logic of the given knowledge still holds: “If you pick an answer to this question at random, what is the chance that you will be correct?” If you randomly pick an answer, the chance of picking (d), the correct answer, is 25%. So (d) is correct. Prove me wrong.

Well, it is 50% because 2 of the 4 options, 2/4, which equals 50%, have the correct answer. You're just never sure if you're going to be right or wrong.

the answer would be 33.33% in this case. The multiple choice is of 4 answers but since 2 options are of the answer there are now 3 options so a 100 divided by 3 is 33.33% hence the answer. However the answer of 33.33% isnt given in any of the options in this question, so no matter what answer u choose the answer will be wrong hence in this case the chance of the answer being correct is 0%

And even if it was given as an option, you would have a 25% chance of guessing it, and since A amd D say 25% those two are correct, but since C says 50% that’s the answer, but since……..

The key word is "random". It can't be 50 because you'd need to use logic to determine there's two 25% answers, so it's a 50/50 shot of choosing the correct one.

It doesn’t tell you to randomly answer this specific question though, it’s asking what would happen if you were to do that. You should still use logic to work it out.

It's 33+1/3% (1 in 3) actually. No paradox here actually. The question is if you pick an answer to THIS question AT RANDOM. So if you just didn't read the question and just randomly circle an answer. Since there's 3 different answer possibilities, there's a 33+1/3% chance to hit the correct one, assuming at least one of them is corect (which is not the case here).

Real chance ls 25% but the thing that is confusing is there are 2 25%s and thus you have a 50 50 chance to pick the right one so that's why the test is confusing

The key here is “if” if you choose an answer at random you would be 50% to get is right bc the answer is 25%. Since you are not answering at random, the answer is 50%.

Given the general assumptions underlying multiple choice questions, this question as presented is a semantic and logical paradox and has no correct answer.

First one to use set theory. And downvoted to oblivion because "set theory is not math and not related with statistics", albeit given the best and correct explanation although a bit convoluted.

Because it’s a 1/4 to select any answer, so it’s 25 But there’s two 25’s, and so 50% of the time You could argue since there’s only one 50%, it’s 25%, but that’s a loop

I kind of think it is 50% since 25% would have been the right answer in a truly random set of 4, but now you have a 50/50 between the two 25% as well. Of course, that only holds true if a or d is correct but not both based on random selection between a and d.

Idk about math but, if two answers are the same or equivalent after simplifying you can assume they’re wrong bc you can only have one answer, standardized test taking strategy. Since you can eliminate a and d I’d say it’s 50%, cause you choose between 2 options

It depends entirely upon the teacher. If the teacher decided one of those answers is correct then the answer is whatever one they decided is right and the percentage chance in choosing it at random is either 20%, 25%, or 1/16, depending on whether you can choose no answer and or any number of answers.

People have pointed out that it's a paradox, so I think the answer is 0%. There is 0% chance you will be right if you picked any of those answers at random, as they're paradoxical.

If the correct answer is 25%, than you have a 50% chance. If the correct answer is 50%, you have a 25% chance. This means that it comes down to how nice the teacher is. If they're very nice, they'll mark A, C, and D as correct giving you a 75% chance of being right. If they're sadistic, they'll mark only A and D or C as right, giving you either a 50% or 25% chance, averaging out at 37.5%. So the true answer to the question is 75% if the teacher's nice, 37.5% if they're not.

The correct answer is both %25 and %50, because the correct answer is %25 but because there are 2 %25’s the chance now becomes %50. But because there is only one %50 answer it goes back down to %25 and rinse, lather, repeat until the end of time

I’m not sure but isn’t it impossible? Because if they were all different you’d know that there’s only one correct answer. But now that there are two options that are the same, you don’t know whether there are two correct answers or just one.

There's only one possible answer, so you have a 1 in 4 chance of randomly picking the correct one. The fact a & d are the same invalidates the question.

The question is if we consider a and d to be both possibly right? Generally, multiple choice questions only have 1 answer unless marked otherwise. If you write down a and the answer was d would you still get the point? If so then the answer is c because you would have a 2/4(50%) chance, but if not you would have to gamble between a and d.

The correct chance (what you actually asked for) is 0%, as neither 50% or 25% are correct as per the other arguments in these comments. However, they’re all trying to give the correct answer, of which there isn’t one. In order for there to be an answer, the probability of picking that answer with a given value has to be equal to that value.

I had a teacher once tell me that the answer to any question is either (c) or the longest answer (most detailed), and that advice got me through high school, so I would go with (c)

Well, it is 50% because 2 of the 4 options, 2/4, which equals 50%, have the correct answer. You're just never sure if you're going to be right or wrong.

If a is correct, 50 percent chance, if b is correct 25 percent chance, if c is correct 25 percent chance, if d is correct 50 percent chance. Given a random one of these is truly correct we average out the percentages to get 150/4 = 37.5 percent chance to pick the correct answer thus making none of them the proper answer unless the probability distribution for the true correct answer is not uniform. In other words not enough information.

So off that bat it’s 25%, but since there’s 2 of those then it becomes 50%, but since there’s one of those, it’s 1/4 chances. Repeat until the end of time, meaning no answer is correct, but a c and d are also not incorrect. Or we can look at it as: we have 3 possible answers (25;50;60), only 2 of which can be correct (25;50). Of those 2 possible answers, if you were to select a random one you have a 50% chance to be correct meaning c. Another possible way to look at it is, since it says at random, the answers available really don’t matter since you are not using available information, meaning you can assume there’s 4 answers of which only 1 is correct, or 25% odds no matter what the answers may be in which case you pick a or d.

This question is meaningless, it have no truth or false value, it asks for the chance for the Correct answer if you pick at random, but the question didn't ask a question with correct or incorrect answer to begin with, sure there's 25% chance for one of the four answers, but it doesn't mean they are correct or incorrect, sorry if this sounds confusing, but that's the best I could do at the moment

its always 25% doesn't matter how many options are 25% because its randomly picked so no matter what you're always picking 1 out of 4 because it's random.

Both a and d should be correct but c cannot be. If you truly guess randomly then you have a 25% chance of getting a correct answer but they are not asking a question so there is no correct answer. 25% isn't so much the correct answer as it is the chance of hypothetically guessing one

But if we choose 50% it ain't random anymore, it's the definitive answer. The premise of the question is choosing an option in random, so there's 2 out of 4 chances of getting it right which is 50%. Then we select 50% as the correct option which ain't random anymore

Easy. This is just one of those questions that has two answers by accident, and once a student brings it to the attention of the teacher they'll tell you to scratch out the duplicate, and maybe even decide to not count the question. So, the answer would be A) or D) depending on which one the teacher tells you to scratch out.

It’s 0%. There are 3 options: 25%, 50%, and 60%. If you had to pick one answer at random you would have a 33% chance of picking the correct one. However since none are 33% you automatically collapse the randomness to 0% since it’s provable that none are the correct answer

But that’s not true because since you have twice as likely chance to hit 25% id the answer is A or D randomly then you have a closer to 50 or 60% chance I’m not sure which

General Discussion Thread

This is a paradox. Because the answer is 25% because there are 4 options. But, because there are 2 options with 25%, that makes 50% chance. However, there is only one 50% option, so 25% chance of getting it right. But there are two 25% options, and so on...

If the 60% answer was 75% it would be better (worse).

I assumed that a correct answer is randomly selected. But now that you point this out I am starting to doubt my solution.

If 60% was 0% it would be that, since the impossibility of a paradox would make no answer guessing, making it a 0% chance

The chance of getting it right is 0%. Which isn't an option, which is why it's true.

So the answer is 0%

A and D are both correct. You have a 25% chance of randomly selecting the correct answer, which is 50%.

Depending on how you look at it you could say that there are two options when selecting between 25% or 50%,

Smort

50%, it's either right or wrong

It's not a paradox. Since none of the listed answers can be considered correct, than chance of getting the question correct by randomly guessing one of them is 0%

Wouldn't it be like this: since there are four options, initial chance is 25%. But, since two options are same, shouldn't the chance go up to 33.33333% instead of 50%.

The answer is a third as there are three options. Since this isn’t an option on the multiple choice, the question is flawed.

I don't think it's a paradox, because it's not actually asking you to answer the question randomly, but rather to report what would happen... if you did that a bunch of times.

The answer is c.

Would it not be 33% since 2 of the 4 answers are the same.

Same as : “True or false: ‘This statement is false.’”

the correct answer is 0%

I disagree,

I don't think this is a paradox. Let me replace the question with a similar one -

This question is purposely a trick

I'm really glad my teachers never pulled this to kinda nonsense

Let me replace the question with a similar one -

It's funny to see that the correct answer changes the correct answer.

Yeah seems stupidly paradoxical

stupidity but evilness is also a thing damn you mrs head! she was a sweetheart

I was thinking about this one for a while. To get the right answer you have to ignore the answers the teacher supplies on the test. Suppose you have 4 objects in a box labeled A, A, B, C and in a second box you have three objects representing the values of the choices A', B', C'. In box 1, P(A) = .5, P(B) = .25, P(C) = .25 and in the second box P(A') = P(B') = P(C') = 1/3. You have to calculate the individual probabilities that your guess will match the correct answer, and then add them together. So P(Correct) = P(A and A') + P(B and B') = P(C and C') = (1/2)(1/3) + (1/4)(1/3) + (1/4)(1/3) = (1/3) so picking one of the four answers has a 1 in 3 chance of success. I'm going to go ahead and agree with the people further down that the true answer is 0%.

I had a chemistry teacher at my Christian high school ask the bonus question “is Hell exothermic or endothermic”

Just tell them it is more than 0% and bingo. You got it right :)

sleight* of hand

If they add a 100% it would be the correct choice as it would be true if it was the correct answer and it is the only one that would have that behavior. Therefore 100% would be the only correct one by process of elimination.

Why stupid? I'd be grateful to have a teacher that puts questions that make your head boggle lol. All questions needn't have a definitive answer

All of the provided answers are incorrect. The answer cannot be A or D because they comprise 50% of the options; as they say the answer is 25%, that's wrong. The answer cannot be C because C is only 25% of the options and it says the answer is 50%, so it's wrong. B is just a random number that has no bearing on anything.

Unless you're a programmer

I would still pick 25 for this reason: the two listed 25s force the answer to be the 50% chance. However in picking 50% the right answer is only still listed once, at a 25% chance of 4 options. So to pick the correct answer (50) is now once again a 25% chance. Where's that two astronaut earth meme when I need it.

Let the answer be x. Note %(S) be the probability that S happens.

EDIT: Another way to think about this is what the probability is for a random number picked from {25,50,60} to match a random number picked from {25,25,50,60}.

No, but now you have a 50% chance of being right if it is 25%

You have shown why none can be correct:

I think so too

I think I solved it. No where in this question does it say you HAVE to pick one of the answer choices for your answer to the question. But it does stipulate that for the random choosing, one of the four answer choices will be chosen. All of the answer choices are wrong, therefore there's a 0% chance to get the answer correct by randomly picking. However, you can still get the question correct by either writing down "0%" or circling a "0%" in either answer choice B or C.

There’s an underlying assumption here that only one of the responses is correct, which leads to a cute little piece of circular reasoning.

Cute?

0%

What if instead of 60% answer B was 0%?

Im propably stupid, but it says randomly. So its like blind choosing. 1 of the 4 must be correct. So if you dont look at the numbers, there is a 25% chance. That means that 1 of the 25% is wrong. We would have to know the exact number of correct answers possible.

There are three answers that you could choose randomly with their respective probability: 25% with 50% probability, 50% with 25% probability, 60% with 25% probability. All of this is wrong.

In my mind, the answer is definitely C.

It's C, because you're either correct, or you're not, and that makes it 50%. Done.

[Warning: my explanation is kinda dumb but it's how I rationalize paradoxes; by avoiding them altogether :) ]

Picking a or d is correct but you only have a 50% chance of being correct. Because this is a trick question and you can pick a b c or d, you have a 25% chance to guess correctly.

There are two questions here, one theoretical, and one practical. These questions have different answers.

It is paradoxical.

I love that everyone has different answers here! Rare for a tdtm. I’ll submit my own to the pile. Here is my claim: (d) is correct. Not (a),(b), or (c). Only (d) is correct. We can verify my claim by checking the logic of the given knowledge still holds: “If you pick an answer to this question at random, what is the chance that you will be correct?” If you randomly pick an answer, the chance of picking (d), the correct answer, is 25%. So (d) is correct. Prove me wrong.

I agree that it's a paradox, but I went in a slightly different direction than most of the top replies...

Well, it is 50% because 2 of the 4 options, 2/4, which equals 50%, have the correct answer. You're just never sure if you're going to be right or wrong.

The inherent conundrum with this question, comes from the fact that people are still reading the answers.

There’s a lot of overthinking in this thread. The problem is about the question and it’s possible answers, not what’s written in the answers.

This feels like it's in a logic class, and I'm going to make some generous assumptions, I think.

the answer would be 33.33% in this case. The multiple choice is of 4 answers but since 2 options are of the answer there are now 3 options so a 100 divided by 3 is 33.33% hence the answer. However the answer of 33.33% isnt given in any of the options in this question, so no matter what answer u choose the answer will be wrong hence in this case the chance of the answer being correct is 0%

And even if it was given as an option, you would have a 25% chance of guessing it, and since A amd D say 25% those two are correct, but since C says 50% that’s the answer, but since……..

The key word is "random". It can't be 50 because you'd need to use logic to determine there's two 25% answers, so it's a 50/50 shot of choosing the correct one.

It doesn’t tell you to randomly answer this specific question though, it’s asking what would happen if you were to do that. You should still use logic to work it out.

It's 33+1/3% (1 in 3) actually. No paradox here actually. The question is if you pick an answer to THIS question AT RANDOM. So if you just didn't read the question and just randomly circle an answer. Since there's 3 different answer possibilities, there's a 33+1/3% chance to hit the correct one, assuming at least one of them is corect (which is not the case here).

Real chance ls 25% but the thing that is confusing is there are 2 25%s and thus you have a 50 50 chance to pick the right one so that's why the test is confusing

No you don’t because there are still 3 answers

The key here is “if” if you choose an answer at random you would be 50% to get is right bc the answer is 25%. Since you are not answering at random, the answer is 50%.

In multiple choice questions there can't be the same answer twice, eliminating "a" and "d" options. Since 2 options left the answer is "c".

Given the general assumptions underlying multiple choice questions, this question as presented is a semantic and logical paradox and has no correct answer.

First one to use set theory. And downvoted to oblivion because "set theory is not math and not related with statistics", albeit given the best and correct explanation although a bit convoluted.

[удалено]

Because it’s a 1/4 to select any answer, so it’s 25 But there’s two 25’s, and so 50% of the time You could argue since there’s only one 50%, it’s 25%, but that’s a loop

I kind of think it is 50% since 25% would have been the right answer in a truly random set of 4, but now you have a 50/50 between the two 25% as well. Of course, that only holds true if a or d is correct but not both based on random selection between a and d.

Idk about math but, if two answers are the same or equivalent after simplifying you can assume they’re wrong bc you can only have one answer, standardized test taking strategy. Since you can eliminate a and d I’d say it’s 50%, cause you choose between 2 options

It depends entirely upon the teacher. If the teacher decided one of those answers is correct then the answer is whatever one they decided is right and the percentage chance in choosing it at random is either 20%, 25%, or 1/16, depending on whether you can choose no answer and or any number of answers.

People have pointed out that it's a paradox, so I think the answer is 0%. There is 0% chance you will be right if you picked any of those answers at random, as they're paradoxical.

If the correct answer is 25%, than you have a 50% chance. If the correct answer is 50%, you have a 25% chance. This means that it comes down to how nice the teacher is. If they're very nice, they'll mark A, C, and D as correct giving you a 75% chance of being right. If they're sadistic, they'll mark only A and D or C as right, giving you either a 50% or 25% chance, averaging out at 37.5%. So the true answer to the question is 75% if the teacher's nice, 37.5% if they're not.

and assuming that a teacher has a 50% chance of being nice, that averages to a 9/16 chance?

The correct answer is both %25 and %50, because the correct answer is %25 but because there are 2 %25’s the chance now becomes %50. But because there is only one %50 answer it goes back down to %25 and rinse, lather, repeat until the end of time

I’m not sure but isn’t it impossible? Because if they were all different you’d know that there’s only one correct answer. But now that there are two options that are the same, you don’t know whether there are two correct answers or just one.

There's only one possible answer, so you have a 1 in 4 chance of randomly picking the correct one. The fact a & d are the same invalidates the question.

The question is if we consider a and d to be both possibly right? Generally, multiple choice questions only have 1 answer unless marked otherwise. If you write down a and the answer was d would you still get the point? If so then the answer is c because you would have a 2/4(50%) chance, but if not you would have to gamble between a and d.

well, logic wise it must be 50% no matter what, since 60% doesnt add up to any x/4 answers, and since 25% are repeated they cant be right

Thecnically It is a paradox, but If we stop the numbers moving around we can mark 25.

The correct chance (what you actually asked for) is 0%, as neither 50% or 25% are correct as per the other arguments in these comments. However, they’re all trying to give the correct answer, of which there isn’t one. In order for there to be an answer, the probability of picking that answer with a given value has to be equal to that value.

The only ways I can think for this MCQ to have an answer would be if there was:

I think the right answer is 33.333333% and it's not listed.

I had a teacher once tell me that the answer to any question is either (c) or the longest answer (most detailed), and that advice got me through high school, so I would go with (c)

It's actually not a paradox, hear me out.

Well, it is 50% because 2 of the 4 options, 2/4, which equals 50%, have the correct answer. You're just never sure if you're going to be right or wrong.

I don't think any of these options are correct. Since 25% appears twice, there is a 1/3 chance of selecting the right answer, making it a 33.3% chance

If a is correct, 50 percent chance, if b is correct 25 percent chance, if c is correct 25 percent chance, if d is correct 50 percent chance. Given a random one of these is truly correct we average out the percentages to get 150/4 = 37.5 percent chance to pick the correct answer thus making none of them the proper answer unless the probability distribution for the true correct answer is not uniform. In other words not enough information.

So off that bat it’s 25%, but since there’s 2 of those then it becomes 50%, but since there’s one of those, it’s 1/4 chances. Repeat until the end of time, meaning no answer is correct, but a c and d are also not incorrect. Or we can look at it as: we have 3 possible answers (25;50;60), only 2 of which can be correct (25;50). Of those 2 possible answers, if you were to select a random one you have a 50% chance to be correct meaning c. Another possible way to look at it is, since it says at random, the answers available really don’t matter since you are not using available information, meaning you can assume there’s 4 answers of which only 1 is correct, or 25% odds no matter what the answers may be in which case you pick a or d.

This question is meaningless, it have no truth or false value, it asks for the chance for the Correct answer if you pick at random, but the question didn't ask a question with correct or incorrect answer to begin with, sure there's 25% chance for one of the four answers, but it doesn't mean they are correct or incorrect, sorry if this sounds confusing, but that's the best I could do at the moment

its always 25% doesn't matter how many options are 25% because its randomly picked so no matter what you're always picking 1 out of 4 because it's random.

At random does not mean with equal probability.

At random? How do you choose something randomly? Either way, I'd still go with either of the 25%s ya got there strictly because they're the lowest.

Both a and d should be correct but c cannot be. If you truly guess randomly then you have a 25% chance of getting a correct answer but they are not asking a question so there is no correct answer. 25% isn't so much the correct answer as it is the chance of hypothetically guessing one

This was my assumption. The question is flawed, I think it's a trick question with no answer as there is no question?

But if we choose 50% it ain't random anymore, it's the definitive answer. The premise of the question is choosing an option in random, so there's 2 out of 4 chances of getting it right which is 50%. Then we select 50% as the correct option which ain't random anymore

Its a paradox because the real awnser is not available in the current pool of options.

Easy. This is just one of those questions that has two answers by accident, and once a student brings it to the attention of the teacher they'll tell you to scratch out the duplicate, and maybe even decide to not count the question. So, the answer would be A) or D) depending on which one the teacher tells you to scratch out.

It’s 0%. There are 3 options: 25%, 50%, and 60%. If you had to pick one answer at random you would have a 33% chance of picking the correct one. However since none are 33% you automatically collapse the randomness to 0% since it’s provable that none are the correct answer

But that’s not true because since you have twice as likely chance to hit 25% id the answer is A or D randomly then you have a closer to 50 or 60% chance I’m not sure which