Results on blind MCQ test

#1
Hello all

I am currently studying for university exams and stumbled upon a theoretical question while my mind was wandering (the question having nothing to do with my studies as I am in the accounting department).

It has to do with multiple choice question (MCQ) tests. I wanted to figure out what the probability is for achieving a certain score on a MCQ test is if you have no idea which answers are correct and thus answered the test blindly.

Suppose that the test consists of y number of questions and each question has n number of options with only one option being the correct answer for a given question.

I though about approaching the situation by thinking of decision trees. Each branch of each question has an equal chance of being chosen (from the test being answered blindly). I came up with an equation but want your ideas and opinions on the applicability/accuracy of my solution.

Attached is a pdf summarizing my work and demonstrating the results using two graphs. I think I am onto something seeing as my cumulative distribution curves all end at 100%, but I am no statistician. Just curious... Thanks in advance for your help.
 

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