When do we trust out guts?

This blog post is about a concept I am defining as 'The Intuition Line'. I am sure I am not the first to do so, but it is currently present in my thoughts so I wanted to write it down! In short, I am defining the intuition line as the point at which intuition stops working for students and needs to be replaced with logical analysis. This comes to mind primarily because of recent work my students and I have done on Probability. As well as this I am struck by the number of questions I see that appear to fall one side or the other of this line. It is perhaps best to start by stating an example of what I am talking about.

The question, 'what is the probability of throwing a 6 on an ordinary dice?' seems to draw an intuitive correct response - If the question goes on to ask, 'what is the probability of throwing two 6s?', this tends to draw an incorrect intuitive response.

All I wish to do really is to ask people to think about when and where this intuition line occurs. How different is it for different people? How is the position of the line affected by teaching? How much of any given exam can a student answer with intuition?

I dont think I can answer these questions yet, but I really think they need answering! I'd welcome any thoughts........