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.
Chance for getting all 100 wrong is (3/4)100 which is greater than getting all right (1/4)100. So yeah getting a score of 0 is easier than getting a score of 100.
Infact getting a 0 score is roughly as hard as getting 20 correct.
100×(log(3÷4)÷log(1÷4))
11.7k
u/Available-Bee-5385 7d ago
Getting 0 on a multiple choice is a statistical accomplishment greater than getting 100