Saw this in a TV show recently where a student took a test and got exactly 0%. The teacher said it’s mathematically impossible. On a multiple choice test if you just guess you should get about 25% and the fact that she got every single question wrong proves she knew the right answers every time.
The teacher is confusing possibility with probability. 0% on a multiple choice test is possible, if you are extremely unlucky. Suppose it had 10 questions with 4 answer choices each. The probability that you get zero, from random guessing is 0.75^10 = 5.6%. That's about the probability of rolling the automatic loss in Craps on a standard pair of dice, i.e. a roll that is either "snake eyes" (2) or "boxcars" (12). Set up 100 students to do random guessing on this test, and it is realistic to expect that five or more of them will get a zero.
It also could be possible, if there is a red herring written in every question, that increases the odds of picking a wrong answer. So much that it is at least equally likely for a student knowledgeable about the subject material to get the wrong answer, than to get the correct answer. As an example, "There is a jar with 5 marbles, and you take 3 away, how many marbles do you have?". One might think a run-of-the-mill subtraction problem and the answer is 2 marbles. But it is a trick question, because "you" are the one who took them, so the correct answer is 3 marbles.