Let me refer you to Figure 1.1, below.
Figure 1.1 shows the probability distribution of a student’s grade on a 20-question, 4-option (ie select A, B, C, or D) multiple choice test, given that he/she didn’t study or even read the questions. That means the grade you’d expect with strictly random guessing. Notice two things: even without reading the questions, you’re most likely to score a 5/20, which means you’ll pick the correct answer 1 out of 4 times. Makes sense! Notice the probability of scoring a 0 – ie being so unlucky that you don’t choose the right option even once – is just above 0%. To be exact, it’s 0.3%. The odds of getting a 0 on my final exam is a third of 1 percent, GIVEN THAT YOU DIDN’T STUDY OR EVEN READ THE QUESTIONS. One student did it. And to make matters worse, I gave out the exam a week before they took it.
Cheers to all the teachers out there who still fight the fight anyway.