Representative Sampling¶

Summary¶

A technique for making probability problems intuitive by thinking in concrete counts ("4 out of 100") rather than abstract percentages or formulas.

Why It Works¶

Kahneman and Tversky found that asking "how many out of 100" instead of "what percentage" dropped reasoning errors from 85% to 0% in the Linda problem. Concrete numbers kick our intuitions into gear.

Examples¶

Steve the Librarian¶

Instead of: "The prior is 4.8% and the likelihood ratio is 4:1" Think: "Out of 210 people (200 farmers, 10 librarians), 4 librarians and 20 farmers fit the description. So 4 out of 24 = 16.7%."

Breast Cancer Screening¶

Instead of: "The posterior is 25%" Think: "Out of 100 women, 1 has cancer (detected), 3 get false positives. So 1 out of 4 positive results = actual cancer."

The Linda Problem¶

Description of Linda (philosophy major, anti-nuclear activist). Asked: what's more likely? 1. Linda is a bank teller 2. Linda is a bank teller AND active in feminist movement

85% chose option 2 (impossible — it's a subset of option 1). When rephrased as "out of 100 people like Linda, how many are bank tellers vs. feminist bank tellers" — nobody made the error.