I'm new to academia SE and I'm not sure if this question fits here, but I think this is the best place I can ask. Please let me know if this question doesn't fit here and suggest me better place to ask.
Let's say that I'm a teacher and there is a student. We ASSUME that if a multiple choice question is given, then we can predict the probability for each choice that the student will choose. For example, if a question have 4 choices A, B, C, and D, then we can predict that the student will choose each answers with probabilities 40%, 30%, 20%, 10%. We will always assume that A is the correct answer. Then my claim is the following:
For education, it is better to give a problem with probabilities 50%, 50%, 0%, 0%, than 25%, 25%, 25%, 25%.
The intuition behind this claim is the following: if we give a question with same probabilities for each choices as 25%, then the student might randomly guess, and she may learn less from solving the question. However, when a student faces a problem with probabilities 50%, 50%, 0%, 0%, then she may choose between A and B. Here 0% means that she (almost) surely knows that C, D can't be an answer. If she did wrong (choose B instead of A), then she may learn more from it because she only need to see difference between A and B.
I want to find a suitable reference that justifies my claim, with some real experiments. I tried to search hard but I failed to find it. If anyone knows such reference (papers or whatever), please introduce it to me. Thanks in advance.