I’m interested in estimating the probability of collusion and cheating on online evaluations.
I also mentioned that there might be a possible solution already out there. I spent some time searching for if someone else was trying to solve this problem and came across a relatively somewhat analogous situation--click on this link, Model, for its specification. At the bottom of this particular page, there is a link to a formula on Wolfram Alpha that might prove helpful.
So, essentially, I have the following questions about the probability, given a class of 40 students, of the following situations:
(1) Assuming that 2 students from a class of 40 take a quiz simultaneously, side-by-side, the probability that the same question overlaps on each student’s quiz is approximately _?
(2) Assuming that 2 students from a class of 40 take a quiz simultaneously, side-by-side, the probability that 2 or more questions overlap on each student’s quiz is approximately _?
(3) Assuming that Student A takes taken a screen capture of each of the 10 questions on his quiz attempts, the probability that 1 question would overlap with the quiz subsequently taken by Student B--his friend who planned to cheat by using Student A's screenshot file) is approximately _?
(4) Assuming that Student A has taken a screen capture of each of the 10 questions on his quiz attempts, the probability that 2 or more questions would overlap with the quiz subsequently taken by Student B--(his friend who planned to cheat by using Student A's screenshot file) is approximately _?
Operationally, I have developed 300 to 500 questions that test material slated for a particular chapter quiz. The full set of questions is then divided among various individual test banks-—each bank holds 20 to 150 questions.
The Canvas leaning management system lets me use the various test banks to design a presumably unique quiz for each student. That is, Canvas enables selecting “X” number of questions from the “Y” questions that comprise all test banks linked to a particular chapter.
For example, to design a quiz for Chapter 1, based on the 393 questions that make up the corresponding Chapter 1 test banks, I set Canvas to execute the following routine: Choose, on a student-by-student basis, 4 question from each of the 5 question banks that collectively comprise all questions for Chapter 1.
Canvas then builds a 20 question quiz by randomly selecting:
• 4 questions from the 60 questions that comprise Bank 1 • 4 questions from the 110 questions that comprise Bank 2 • 4 questions from the 78 questions that comprise Bank 3 • 4 questions from the 104 questions that comprise Bank 4 • 4 questions from the 41 questions that comprise Bank 5.
Ultimately, Canvas randomly generates a one-of-a-kind 20 question quiz from the 393 questions that comprise the 5 question banks for the Chapter 1 quiz.
Thank you.