This is how good intuition is developed.
Originally Posted by Orobas
You learn, for yourself, "what your bad intuitions sound like." There are certain intuitions that almost always lead you astray. I, too, have learned to assume that most people have good intentions, that most people believe they are being reasonable, and my predictions are far more accurate if I make these assumptions and only alter them in exceptional cases.
At more advanced levels, it helps to understand probability theory, statistical selection effects, and so on, to filter out the crap. In particular, statistical selection effects will introduce "trends" in your data (intuitive or otherwise) that make things look different from reality, that introduce rules and assumptions that are false and potentially misleading.
Probability theory helps to point out where things can "sound like" one thing, but are really something else. Consider the following probability problem:
You are on an plane trip, sitting next to a man you just met. During the course of conversation, he mentions that he has two children. One of his children is a boy. What is the probability that the other child is a boy?
Most people will answer, 1/2. 50%. This is the wrong answer.
The correct answer is 1/3. 33%.
The probability space is boy-boy, boy-girl, girl-boy, girl-girl. The conditions of the problem eliminate only the girl-girl possibility. Of the remaining possibilities, two have the other child as a girl, one has the other child as a boy. Hence, 1/3.
If the problem were phrased, "His oldest child is a boy," instead of, "One of his children is a boy," then the probability would be 50%.
Storing this kind of reasoning as part of one's intuitive understanding makes one's intuition far more accurate. And what you store isn't "oh, in this kind of probability problem, the probability is 1/3, not 1/2" ... rather, you store "very subtle word changes can totally alter the boundary conditions of the problem; look for those subtleties and check to see if they drastically change your intuitive conclusions."