This is an oldie, but a good one. You've probably come across it in an IQ test at some point. Consider the following statement:
Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Based on the information above, which of the following statements do you think is more likely?
A. Linda is a bank clerk.
B. Linda is a bank clerk and is active in the feminist movement.
If you answered B, you are are wrong but in good company. When this has been tried in experiments in the past something like 80% of those asked went for B. But it is quite obviously wrong, in terms of probability, when you think about it for second. Bank clerks who are feminists are subgroup of bank clerks as a whole. The probability of Linda being both a bank clerk AND a feminist must be lower than the probability of her only being a bank clerk. In real life the best you could hope for (to justify your belief) is that all bank clerks are feminists. In mathematical terms you are simply wrong.
This is something known as the conjuction fallacy. The reason why we get it wrong, the bias in our thinking, is known as the representativeness heuristic. We think that B is more likely because that option seems to 'represent' Linda more, based on the information we have. Notably this has has also been tested in policy circles, and the experts get it wrong too, because they too look for 'representativeness'.
Another example - if you were asked what you think the probability is that the US would invade Saudi Arabia next year, I assume you would give it a fairly low score. But what if I asked you the probability that there was a major terrorist attack on the US linked to the Saudis, and the US subsequently sent in troops? In mathematical terms the former is more likely, but the latter 'feels' more likely doesn't it?
To me this is another reasons to take seriously the central idea of the narrative paradigm that we are primarily engaged in story-telling. A lot of the information we are given is simply a convincing story that fits the facts, but if you try and apply some basic probability assessments to what you are being told you'll find that some explanations are a lot less plausible than they appear on first glance.
I think this is pretty important stuff. In politics we are repeatedly drawn to conspiratorial interpretations of why certian things have happened, and I think that a lot of this is driven by the representativenes heuristsic. It maybe more boring as a way of looking at events, but it strikes me that in probability terms cock-ups are often the real story.