Understanding probability intuitively has been the focus of a lot of research in empirical economics. In many cases we form an opinion intuitively, then give reasons as to why its right. We don't form the opinions rationally, using math etc., then understand them intuitively. Probability and statistics professors who are tested (read Taleb or Kahneman etc. - spelling?) do well on the math, but ask them a real world problem and they typically get it wrong. This is empirically measurable. Intuition is high associative, and leads to confirmation bias.