I’m currently facing a situation that I need some help about. So here is the problem.
Let’s say we have a question bank with N questions, where in each question has a defined probability score that tells the question’s capability of segregating good/bad students out of the pool of students who took that question. Essentially this is a conditional probability in form:
P(Good Student/Question answered correctly)
This probability has been calculated based on past data.
Now, I want to calculate the similar probability score of a question paper that has been created by selecting N questions from Question Bank. As per my understanding, this is the case of
P(A and B and C .... and N) wherein A is probability of question 1 answered correctly and so on. Considering questions are mutually exclusive (not sure about this though).
However, the problem with this approach is that the end probability after selecting N questions would be very small and I don’t think that is the appropriate probability.
So how should I combine the question’s individual probabilities to come up with one final probability for the overall question paper? Please let me know in case any other detail is required to understand the question better.
Looking forward to any help and thanks in advance!