But you are assuming there exists a positive correlation between absence of brown M&M:s and whether the other demands are also filled or not. I don't think you

But you are assuming there exists a positive correlation between absence of brown M&M:s and whether the other demands are also filled or not. I don't think you can show that since the M&M demand was singled out. Yes, that is the assumption. Many mathematical models make assumptions like that. It seems much more likely than the opposite assumption which is that they are independent. Since you're attempting to model human behavior you are going to have to make assumptions that are ultimately incorrect. That's how humans process information. We join the dots and infer things in countless ways that mean we could be incorrect, but which none-the-less are better than wildly guessing (http://en.wikipedia.org/wiki/List_of_cognitive_biases http://en.wikipedia.org/wiki/List_of_cognitive_biases). It would be probably better, if you are trying to model this, to think of it as a machine learning classifier. Brown M&Ms existing would be a prominent feature, not proof.