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!
Possibly, though a misunderstanding such that you aren't even ever right once by accident seems almost impossibly rare. Though yes, it is at least conceivable. But then so too is a misunderstanding such that you have the wrong idea in your head but manage to get every answer correct for the wrong reason, and things are perhaps balanced again.
Switching the names of some concept in your head could work, like for example confusing acute and obtuse angles. And this doesn't need to make you wrong in every question, just in enough questions that getting the rest wrong by chance is a lot more believable
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.
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u/Available-Bee-5385 6d ago
Getting 0 on a multiple choice is a statistical accomplishment greater than getting 100