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.
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
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.
We had this problem for real when the school insisted on giving 1st year Spanish students the final exam going in. We really wanted all of them to get a 0, but of course that's not what happened, even when they genuinely didn't know any Spanish.
The joke is that in the movie Spider-Man: Into the Spiderverse the main character (Miles) intentionally is trying to seem stupid, and so purposefully gets all the answers wrong on a true/false test. He still gets 100% because the teacher runs the numbers and tells him that getting either zero or one-hundred through guessing every answer are equally unlikely, so he clearly didn’t do that.
This test is a multiple choice test which means the odds of getting a zero by guessing are much higher and the odds of getting full marks are astronomically small - therefore the logic that says Miles wasn’t guessing doesn’t hold up.
However if the entire human history of 117bn .. and everyone too 5.85e7 tests in their lifetime.. then statistically you'd get 1 randomly perfect score.
So if you lived for 40 years and did tests everyday.. that's 4006 tests per day, or 333.9 per hour assuming 12 hours a day.
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.
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.
If we're being pedantic, you have to calculate the odds of a student getting all the questions wrong when they're trying and not when they're guessing.
We're taught from birth to try to get all the right answers.
So a student getting all the wrong answer not by choice or by chance but by being confidently incorrect on every answer. Now THAT is a statistically unlikely event.
Not to nitpick (well, Ok actually TO nitpick), the 2nd column starts with 19, thus we might assume 36 questions, which adds a some zeros to both of your answers:
0.75 ^ 36 = 0.000031
0.25 ^ 36 = 2.118×10⁻²²
So odds of getting all wrong if choosing randomly is around 3 in 100,000.
Definitely rare enough to call in a student and ask why they are deliberately missing them all. And to assume they must know all the correct answers in order to do this.
Though also you're right this COULD happen by chance occasionally. Assume your school has 4000 students and when faced with a multiple choice test, 1% ALWAYS use the strategy of choosing answers randomly. And they have such a test with 36 answers or more once a week.
(Which is probably massively overestimating it - people who aren't even going to try are far more likely to just leave the test blank than go to the work of filling all blanks with a random answer. They're also likely to mess up here and there by leaving a few blank or whatever - we're talking about the people trying LEAST hard hear, not MOST hard.)
Assuming 40 weeks/year, after 50 years you've had 80,000 examples of randomly answered tests, and with 3/100000 odds you've got a reasonable likelihood of no correct answers happening once or twice.
100
u/South_Bit1764 12d ago edited 12d ago
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.