Thinking, Fast and Slow

by Daniel Kahneman

A random event, by definition, does not lend itself to explanation, but collections of random events do behave in a highly regular fashion. Imagine a large urn filled with marbles. Half the marbles are red, half are white. Next, imagine a very patient person (or a robot) who blindly draws 4 marbles from the urn, records the number of red balls in the sample, throws the balls back into the urn, and then does it all again, many times. If you summarize the results, you will find that the outcome “2 red, 2 white” occurs (almost exactly) 6 times as often as the outcome “4 red” or “4 white.” This relationship is a mathematical fact. You can predict the outcome of repeated sampling from an urn just as confidently as you can predict what will happen if you hit an egg with a hammer. You cannot predict every detail of how the shell will shatter, but you can be sure of the general idea. There is a difference: the satisfying sense of causation that you experience when thinking of a hammer hitting an egg is altogether absent when you think about sampling.