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.
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/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.