Conjunction Fallacy

Probability and chance often appear to be counterintuitive…Consider the following scenario:

John initially took a degree in mathematics, and followed it with a PhD in astrophysics. After that, he worked in the physics department of a university for a while but then found a job in the back room of an algorithmic trading company, developing highly sophisticated statistical models for predicting movements of the financial markets. In his spare time he attends science fiction conventions.

Now, which of the following do you think has the higher probability?

A. John is married with two children.
B. John is married with two children, and likes to spend his evenings tackling mathematical puzzles and playing computer games.

Many people answer B. In fact, the set of people described by the characteristics in B is a subset of those described by the characteristics in A: for John to have the characteristics of B, he has those of A and more. It follows that the probability that John is described by B cannot be larger than the probability that he’s described by A.

…This failure of intuition is often called the conjunction fallacy.

From The Improbability Principle by David J. Hand.
It’s a fascinating look into just how poor we human beings are at predicting outcomes. My favorite bits of the book are when Mr. Hand savages Carl Jung for casting a broad net over his personal coincidences as evidence for synchronicity. Sure, that’s low-hanging fruit these days, but still makes for good reading.