After completely guessing on quite a few tests (long story here), I've always wanted an accurate estimate of my scores, but I could never apply the probability theorems I learned in high school. I've never taken a formal course pre or post calculus statistics (nor have I taken calculus), but I find great curiosity in problems like these. It's totally fine if you use ridiculously hard math to explain, because I believe that someday I will come back and look at this problem again.
Here's the basic problem, and following are a bunch of variations that could be added to the problem.
Let's say I have 60 multiple choice questions each with 4 choices and that the total score is 100(%). Now, 20 of those questions are 3 points each, and 40 are 1 point each. Let's say that answer distribution is equal among the four choices (A,B,C,D). How would I find the probability of getting a score n, given that I randomly selected choices?
Variations: How would I calculate the probability of n if answer distribution was not equal, but normally distributed? If so, how would I calculate the probability of n if I chose equal answers, or in general, answers with restrictions?
This might not be an effective problem to solve with known probability theorems; I don't know. This might be something common for people that are super whizzes at statistics; I don't know either. Please tell me what you know about it though. Thanks!