I'd like to know how to calculate the following. Given M proportions for a sample of N multiple-choice question correct answer choices, where each of the questions has M answer choices 1st to Mth, what is the probability that the M proportions deviation from 1/M would be seen by chance?
I hope I've stated my question correctly. Example: Given a set of correct answers for N=500 questions each with M=5 answer choices A to E as follows: A 0.223, B 0.191, C 0.196, D 0.185, E 0.205; what is the probability that those results will be observed by chance? Or conversely, what is the probability that the test producer's choices of assignments of correct answers to letters A to E was biased?
(I have access to RStudio but it's been a long time since my minimal use of R.)