85% of people get this wrong—including statistics experts! The Conjunction Fallacy shows how our intuitions about probability systematically fail.
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.
B is a SUBSET of A. P(A and B) ≤ P(A) ALWAYS!
We judge probability by how well something matches our mental prototype. Linda's description SOUNDS like a feminist activist, so "bank teller + feminist" feels more likely—even though adding ANY condition can only reduce probability. Our intuitive "System 1" overrides logical "System 2" thinking.
Daniel Kahneman and Amos Tversky published this in 1983 as part of their groundbreaking work on cognitive biases. Kahneman later won the Nobel Prize in Economics (2002).
The Math: P(A and B) ≤ P(A) is a fundamental rule of probability. If Linda must satisfy BOTH conditions, the probability can only stay the same or decrease—never increase.
Real-World Impact: This fallacy affects jury decisions, medical diagnoses, financial predictions, and everyday reasoning. Detailed scenarios feel more plausible even when they're mathematically less likely.
"The more specific the scenario, the more likely it seems—but the less likely it actually is."