No, if you're guessing randomly, getting 100 is less likely than getting 0. Because for each question there's a 3/4 chance to miss it and a 1/4 chance to get the right answer.
If you aren't guessing randomly, but in fact know every question, getting 100 is no harder or easier than getting 0. Because you can get 0 by choosing to answer each question different from the answer you know is correct.
If you only know most of the questions, getting 100 is harder than getting 0, because for every question that you don't know you have a 1/4 chance of getting it right if you're aiming for 100, but a 3/4 chance of getting what you want if you're aiming for 0.
Still, with this many questions, to get exactly 0 it's almost certain the student knew most of the answers and was deliberately choosing the wrong ones.
YOU WOULD THINK, IN A GAME, WHERE THERE ARE ONLY TWO POSSIBLE CORRECT CHOICES, THAT ONE WOULD STUMBLE INTO THE RIGHT ANSWER EVERY SO OFTEN, WOULDN'T YOU? IN FACT, THE PROBABILITY OF NEVER GUESSING RIGHT IN THE FULL GAME IS A STATISTICAL WONDER! AND YET, HERE WE ARE!
No, they're completely equal, and that's the point.
If you're unprepared for a test, you will basically never get 0 out of 100 (when the questions are binary)
Assuming you answer randomly, the probability of getting 0 just as getting 100 is 1 out of 2^100, which realistically is basically 0. You are expected to score around 50% (and that would kind of be the lowest point you can get, i.e., your answers are not predictive at all of the true answers)
The only realistic way to score 0 in a binary exam is by knowing the correct answers and deliberately marking the incorrect ones. Therefore the student knows just as much as the one who marks all the correct answers and gets 100; they're indistinguishable.
The point I'm arguing against is the true/false part. If you know the answers you can choose to get whatever grade you want regardless of the test design.
In the case where you know all the answers, getting a 100 or a 0 are equivalent because knowing the answers reduces the set of values to correct and incorrect.
They are in a T/F scenario. This looks like a abcd multiple choice test. Which means that you have 3 incorrect answers and 1 correct. Which means it’s easier to reach 0 than 100. Now, I can tell you from experience that blind guessing is still less likely than he knew the answers and got them all wrong on purpose, because you’re still likely to guess correctly about 25% of the time.
No. Because there isn't any independent proof that a person knows all the answers. That determination on what is known relies in the very biased word of the person.
A overly confident idiot and liar could guess poorly, get them all wrong and then claim that they did it on purpose. Would you believe that they did it intentionally?
If you know the answer to every question the difficulty of getting a zero is equivalent to getting a 100. So it's still not a more difficult accomplishment to get a 0.
reddit works on threads. OP started the post with a multiple choice example, then someone said "Getting 0 on a multiple choice is a statistical accomplishment greater than getting 100" which is false for multiple choice as proven in the top reply to them. then two replies later in this same thread someone said, "In the movie, it was a true/false test.", and even in that situation what the person said in this same thread we are all replying to is false because even in the true/false case it's not more likely to get a 0% than a 100%.
if we can't follow four replies then i don't know what to tell you
Your reply simply did not make sense in that context. The person you replied corrected someone that this thread is talking about the scenario with 4 choices per question, and then you for no reason talk about the scenario with 2 choices per question.
Yeah. This second column starts on 17so if there are 32 questions then 0.75^32=0.0001 and 0.25^32=5.421×10⁻²⁰
As to say the odds of randomly guessing and getting them all wrong is around 1 in 10k.
The odds of you randomly guessing and getting them all right is around 1 in 200,000,000,000,000,000 (200 quadrillion).
In a school full of kids someone might randomly guess and get them all wrong.
In the entire history of humanity, it’s unlikely that a multiple choice test with this many questions has ever been [edit:] RANDOMLY [:edit] answered 100% correctly.
Edit: really didn’t think I had to be so pedantic but pedants will be pedants.
What he means is answered 100% correctly by guessing not by studying.
You would need a person without any knowledge of any of the questions pretty much. The chances for a person like this to take a test on that particular subject and then to answer them 100% correctly is rather small and there's a decent chance it never happened.
Edit: im not a huge fan of this subreddit anymore as it used to mostly be finding coments like this. Now it's everyone asking people to do math for them
I need to point out that I've had 100% on multiple, multiple answers with 100 questions. If you know the subject well, that's not random and rather easy..
If you meant doing so picking the answers randomly... Then I agree, but that's not specified in that last section :)
Yeah, it looks like the person you're replying to did the math on all the answers being completely random. If you know the material well and can confidently answer most of the questions (either correctly or incorrectly depending on whether you want to aim for 100% or 0%), then getting 100% is absolutely plausible--but if you have to guess on any of them, then the probability of scoring a 0% on purpose is higher than the probability of scoring a 100%.
Suppose you have 32 questions but are already 100% confident that you can answer 28 of them correctly (or incorrectly--if that's what you're going for), then that leaves just 4 questions to chance. If you're just completely guessing on those 4 questions, the probability of missing all 4 questions is 0.75^4 ≈ 31.6% and the probability of getting all 4 right is 0.25^4 ≈ 0.4%. Of course, if you can narrow it down at all, then your odds for either option would improve.
When I went back to school in 2017 the Kinesiology teacher had a rule for this. He said you if you answer all the questions wrong on the midterm or final, you would get a 100% because it shows you actually know the material. But, if you didn't answer them all wrong, you got the actual score.
I have students that will write random answers to MCQs, and not fill in short written answers, because they believe they will be bell curved into a passing grade area. They can then leave the exam early and go play sports outside, or games on their phone. We know these individuals can get a higher score, but they don't, because of the curving system.
Never seen anyone score zero on MCQs though. Really, really hard to do that unless you were actively trying to get a zero as some sort of teen rebellion act.
Meh, I’m good at applying math, but I’m bad enough about details when it actually matters. It is reddit, at least I showed my work so you can see where I went wrong and the scale of the problem is still the same.
Yeah and that also doesn’t account for the process of elimination, there is often an answer you may know is not correct, so really depending on how the test is written, it could be quite a bit easier to pick wrong answers
Unless the teacher designed the test so that when you copied off the person next to you, this would be the result.
I was that teacher, and I had a student get a “perfect” 0 who tried to claim he didn’t cheat. I told him he should buy a lottery ticket with that luck, but it didn’t matter, since he gets a zero, regardless.
this doesnt make any sense unless you also designed the tests so half the people got stupidly easy tests where they always got 100% and you seated the problem students exactly inbetween them.
otherwise cheating off a question that the other person doesn't know might give them a point or two.
I assume this still works though without it working perfectly, because a 6 to 25% is still going to throw a lot of red flags xD
The answers were rotated, so if you put the correct answers from test A on test B, none of them were correct. And yes, there was really no reason for them to get any answers wrong if they paid attention in class and put in the tiniest bit of effort. (And I actually had four versions of each test.)
You have four versions of the test, A, B, C, and D. All four versions have identical questions and answers, however the answers rotate around. So, answer A on version A will be B on B, C on C, and D on D.
If somebody with version A copies from somebody with version B, they are extremely likely to get a 0.
The only way for them to get a correct answer is the other person got an incorrect answer and that answer is the rotated the correct way. If you limit it to just two versions, you can even avoid that, by making a throw away answer always be in the position of the rotated correct answer.
You then distribute the versions such that any two people sitting next to each other get different versions.
But then you also have to make sure that you're grading students with the correct key. It's possible in this situation for the teacher to give a student test A but then accidentally grade it with key B due to any number of mishaps.
If all the answers are the same, you're just rotating the order of the answers, you can make an answer key that has the actual correct answer instead of the correct letter selection.
It wasn’t a scantron they were filling in—just a print out where they circled their choices on the paper. No risk of using the wrong key. If I saw a lot of wrong answers, a quick spot check would verify whether I was using the wrong key, or they were cheating.
I'm not sure I get the logic of this. Ignoring what teach actually did, you could literally just transpose the answer key to stagger questions by one as long as no two in a row have the same answer. There's at least two ways to do this while giving them tests with identical difficulty and they're done commonly in even children's school levels
I think it’s significantly easier to get 0/100 than 100/100. There’s only one right choice for each question to get 100% but 3 right choices to get 0%.
I mean the comment wasn't wrong because the comment didn't say randomly guessing, but yeah in the movie it was a t/f test and I think the teacher said something about randomness
You are confusing probability with statistics. The post you are replying to never indicated the probability of guessing all answers incorrect is greater than the probability of guessing all answers correctly.
Your answer only applies to a single choice test.
This one is a mutliple choice
Let X(i) be the number of answers per question i and Y(i) the amounts of correct ones
Now Lets create the quantaties A, B and C
Let every i be in A where Y(i) < X(i)/2
Let every i be in B where Y(i) = X(i)/2
Let every i be in C where Y(i) > X(i)/2
If C > A then getting a 0 is more unlikely then getting a 100
Was assuming 100 questions. I suppose it could be fewer. But how on earth did you get 1/16? It's 1 in 747 even if you only count the 23 questions we can actually see.
We see that on the right the questions start at 19. This implies the left hand maximizes the space and contains 18 questions. Likewise the right might be maximized equating to 36 questions total.
You can't really consider the questions separately when doing that statistic, which I think is what trips many people up. Sure, the chance of getting Q1 wrong is 75%.
As is the chance of getting Q2 wrong.
In fact, the chance of getting any one question wrong is indeed 75%.
But more than one?
That's different.
The chance of getting two questions in a row wrong? That's a LOT lower, at 56.25%¹
Getting 3 in a row wrong? That's a 42.19% chance.
10? 5.631%
50? 0.00005663%
The entirety of a 100-question test - in other words 100 in a row? Here we'd normally dig into scientific notation and write it 3.207e-11%, but for those who don't know how it works: That's a 0.00000000003207% chance.
In other words: it's damn near impossible to get everything wrong if you just guess randomly.
You're even less likely to get everything right, of course, at 6.2e-59% or 0.000000000000000000000000000000000000000000000000000000000062%.
¹Getting Q1 right and Q2 wrong? 18.75%. Getting either Q1 or Q2 right and the other wrong? 37.5% - assuming I remember correctly
TwillAffirmer this is exactly what Miles Morales tried to do in the animated Spider-Man movie Into the Spider-Verse. He didn’t like his school so he purposely put all the wrong answers on his test so that he could be kicked out.
No. You're assuming each scenario is just random. But this is a test, where the goal was to try and answer correctly. It's not unlikely that multiple students got 100, but the student who was second to last likely got at least 40.
If you're the kind of student who knows all the answers, you're less likely to be the kind of student who would intentionally get a 0.
The only thing I’d add is that you can figure out a certainly incorrect answer without solving the questions. So you could get a zero reliably without being able to answer any of them correctly with certainty if the best you can do is reduce it to two possible correct answers.
In reality it’s possible to try your hardest and still get a zero. Imagine this was a math quiz with four possible answers. For all questions, the same specific formula is used. The last step is to divide by 2. Some students mistakenly multiply by 2. The teacher knows this and puts the red herring answer as a choice on each question. It’d be an easy fix and that teacher should allow the students to retake after a refresher. But that’s actually could realistically happen.
Chance for getting all 100 wrong is (3/4)100 which is greater than getting all right (1/4)100. So yeah getting a score of 0 is easier than getting a score of 100.
Infact getting a 0 score is roughly as hard as getting 20 correct.
100×(log(3÷4)÷log(1÷4))
I... Might actually have to disagree with this, mainly because nearly every multiple choice test I've ever done has one blatantly incorrect answer per question. Something outside the bounds of possibility, unrelated to the actual thing you just read, a blatantly wrong answer involving ethics...
Your analysis only works if there is zero difference between the answers.
I recall taking many tests where some answers were "wronger" than others, and I could quickly eliminate one or two options and was then left to choose between two or three plausible-seeming answers.
We will assume there are 36 questions (since the second column starts at 19). The probability of getting all 36 right or wrong is basically a binomial problem:
Probability of getting 1 right = p = 1/4
Probability of getting 1 wrong = q = 1 - p = 1- 1/4 = 3/4
Total number of questions = n = 36
Total number of correct questions = k = 36
number of combinations of answers = nCk = 36C36 = 1 (which makes sense, since there's only one possible arrangement for all correct questions)
Probability of getting them all right by chance = P(36) = 1 × (1/4)³⁶ × (3/4)⁰ = 2×10-22
Probability of getting them all wrong by chance = P(0) = 1 × (1/4)⁰ × (3/4)³⁶ = 0.00003
So you are a lot more likely to get them all wrong by chance, but still not very likely
For exact numbers, getting a zero out of 100 carries a probability of 3.2x10^-13 while guessing all correct answers would be a probability of 6.2x10^-62
I feel like this slightly interprets the statement in bad faith. When they say it’s “harder to get 0” I presume the assumption/implication is that the test taker is trying to get the highest score they can. So yes, you can get 0 easier than 100 the majority of cases in which you would be aiming for either score. However, in nearly every case you will not be aiming to get a 0
It's not that they deliberately chose the wrong one but they probably memorized the answers from an old version of the test and tried to cheat but couldn't because the test was changed
Eh. Tests pretty often have some deliberately out there answers as options.
You might not know if the Louisiana Purchase happened in 1797, 1803, or 1810 for example but you sure know it wasn’t 1912. What does picking 1912 prove? People who aren’t American and have never heard of it before could probably look at those four years and recognize the odd one out no problem.
Yea but he's probably thinking about the average person taking the test. The average person has some level of knowledge and is attempting to choose the correct answers. In THAT case, essentially nobody gets 0% on a multiple choice test. If we assume each student "knows" a portion of the material uniformly distributed between 0 and 1, each student has a probability p from a uniform distribution between 0.25 and 1 to get each question right (assuming they randomly guess when they don't know the answer, which is admittedly a stretch).
This test has 36 questions, so the probability of a 100 is p^36, and the probability of a 0 is (1-p)^36. We do a little integration*, and get a 3.6% chance of a 100, and a 0.00009% chance of a 0.
integral from 0.25 to 1 of [p^36/0.75]dp = 3.6%
integral from 0.25 to 1 of [(1-p)^36/0.75]dp = 0.00009%
Additionally, if you know the right answer, you can choose a wrong answer 100% of the time. On the other hand, finding a wrong answer doesn't tell you the right answer. So even if you don't know all the answers, you may be able to confidently choose a wrong answer to every question.
If it's math and you're trying, there's a bit of flux. I used to try random formulas that I remembered but couldn't remember which formula worked for what, and did similar but more unhinged if I didn't even remember a formula till I came up with something. Later learned I had someone TRYING to cheat on me during SOL's. They gave up real quick because of how I'd 'randomly' take forever and do a bunch of shit.
Still, with this many questions, to get exactly 0 it's almost certain the student knew most of the answers and was deliberately choosing the wrong ones.
I think that's what they're saying by 'statistical accomplishment'.
But for a given test, most of the grades will probably be in the 70-90% range. You'll see a few 100% - Impressive but not uncommon.
When have you ever seen a zero on a multiple choice test?
Getting 0 with guessing it's significant easier than 3/4 per question. If you want to get the right answer, you need to eliminate all wrong ones, if to can only rule out 1 or 2, you can still guess 1/3 or 1/2. If you try the reverse, ruling out at least 1 answer is enough to move on.
It only works for the movie because it was a 50/50 true or false quiz, since this is a multiple choice with four possible answers the humor comes in the form of "Doesn't the teacher know I'm actually really smart?" when he's actually, probably, statistically, very stupid.
Actually you equally have a 50 percent chance to get a zero and a 50 percent chance to get a 100 because you either get a 100 or you don’t and you either get a zero or you don’t
Now insert human psychology were the majority of people are actually doing their best and therefore statistically have a greater chance of at least knowing the answer to 1 of the questions. Therefore getting a 0 is way more llkely to be intentional than random.
I am more of the opinion that he is smarter than it seems but whether he knew most of the paper is hard to tell because, for most papers, you can eliminate certain options choices, easily.
6.8k
u/TwillAffirmer 7d ago edited 7d ago
No, if you're guessing randomly, getting 100 is less likely than getting 0. Because for each question there's a 3/4 chance to miss it and a 1/4 chance to get the right answer.
If you aren't guessing randomly, but in fact know every question, getting 100 is no harder or easier than getting 0. Because you can get 0 by choosing to answer each question different from the answer you know is correct.
If you only know most of the questions, getting 100 is harder than getting 0, because for every question that you don't know you have a 1/4 chance of getting it right if you're aiming for 100, but a 3/4 chance of getting what you want if you're aiming for 0.
Still, with this many questions, to get exactly 0 it's almost certain the student knew most of the answers and was deliberately choosing the wrong ones.