I want to create a multiple-choice exam consisting of $N$ problems. Each problem has $M$ mutually-exclusive options. If you don't choose any option, you will get $0$. If you wrongly choose, you will get $-1$. Otherwise you will get $1$.
To pass the exam, at least you need to have a score of $x$ where $0<x\leq N$. When an uneducated toddler plays with the answer sheet and behaves randomly, what is his/her probability to pass? The toddler knows that she/he cannot choose 2 or more options for each problem.
If you think my question is not clear enough, you can make some answers, each for the possible case you think.