Science Puzzle
The Climbing Accountant
Sam is 29, spends every weekend in the mountains, loves hard rock climbs, fixes their own bike and is always up before dawn. You don't know anything else about Sam.
Which is more likely: that Sam is an accountant, or that Sam is an accountant who goes rock climbing?
The Answer
A is more likely. It has to be, whatever the description says.
Every accountant who goes rock climbing is, first of all, an accountant. So the group in statement B sits entirely inside the group in statement A. If Sam is in B, Sam is automatically in A too; but Sam could be in A, an accountant who has never touched a climbing wall, without being in B. Adding an extra condition can only make a statement less likely or leave it the same. It can never make it more likely.
Yet B feels more likely, because it fits the story. The description is full of climbing, and B mentions climbing, so it seems to match Sam better. In 1983 the psychologists Amos Tversky and Daniel Kahneman tested a famous version of this puzzle about a woman called Linda, and 85 to 90 percent of people picked the more detailed answer, even though it was logically less likely. They called it the conjunction fallacy.
The trap matters well beyond puzzles. A detailed, vivid explanation, whether of a crime, a disease or a historical event, can feel more convincing than a plain one, even though every extra detail is one more thing that has to be true.
The principle: The conjunction fallacy. Two things being true together can never be more likely than either one alone, however well the combined story seems to fit.