While there's a mushrooming field of psychology that details how our many cognitive biases make us poor natural statisticians, there are good reasons for our brains not to operate in strictly Bayesian ways.
For one, our brains were designed in a time when relevant numbers rarely went above 150 (the number of people we were likely to encounter in life).
More importantly, back when we all lived on the Savannah, genes would do well to err on the side of being overly-cautious.
The example I gave Bernstein was how you wouldn't really care about sample size or the denominator of a trend when it came to lions: seeing one friend mauled by a lion would be evidence enough that avoiding lions was a good idea. But today I bumped into an xkcd comic that illustrates how, even today, we're more often better off not thinking like scientists or statisticians:
By the way, for one of the best overviews of how our illogical minds do a good job of simulating logic most of the time, take in Kathryn Schultz's Being Wrong.
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