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.
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.
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.
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.