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
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u/TwillAffirmer 12d ago edited 12d 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.