Steve is quiet and tidy. In the US, is he more likely a librarian or a farmer?

A farmer: there are 20+ times more of them. Yes. The description fits the stereotype, but there are so many farmers that the quiet, tidy ones still outnumber all librarians.

What’s more likely about Linda?

She’s a bank teller. Right. “Teller and feminist” is a part of all tellers. A part can’t be more likely than the whole, however well the story fits.

Danya wants to quit school and “trade for a living” after watching videos. What’s the honest starting point?

The base rate: in a big study, 97% of such traders lost money. Right. Honest base rate first, careful adjustment second. A sensible plan: practise on a demo account and don’t drop the main path.

Stereotype vs statistics

Lesson 8 of 31 in the course “Brain Hacks”. Free, with animations and a quiz.

Librarian or farmer?

Steve is quiet, tidy, loves order and detail. Is he more likely a librarian or a farmer? Almost everyone says “librarian”: the description fits the stereotype perfectly. But in the US there are more than 20 male farmers for every male librarian. Even if quiet, tidy people are rarer among farmers, there are still more of them in absolute numbers. Autopilot compares with an image and forgets to ask how many people are in each group at all.

What a base rate is

A base rate answers the question “how often does this happen in general, without the details?”. How many farmers versus librarians, how many startups survive, how many traders make money. The right order of thinking goes like this. First, the base rate. Then: how reliable is the description or the story? Only then do you move away from the base, and carefully. Autopilot does the opposite: it trusts the vivid description right away and skips the first step entirely.

The Linda problem

A famous puzzle. Linda is 31, smart and outspoken, and in college she fought discrimination. Which is more likely: Linda is a bank teller, or Linda is a bank teller and an active feminist? About 85–89% of students, even at top universities, picked the second. But that’s logically impossible: “teller and feminist” is a subset of all tellers, and a part can’t be more likely than the whole. Details make a story feel true, while the probability only drops.

The taxi problem

At night, a cab hit someone and drove off. In the city, 85% of cabs are green and 15% are blue. A witness said the cab was blue, and tests showed that in those conditions he’s right 80% of the time. What’s the chance the cab really was blue? Intuition says “80%”. The correct answer is about 41%. Blue cabs are so rare that the witness’s mistakes about green cabs almost equal his correct calls about blue ones. Without the base rate, even a reliable witness misleads you.

The base rate for “I’ll trade for a living”

Danya watches videos of traders with fancy cars and thinks: “I can do it too.” That’s a description without a base rate. And there is one: researchers looked at everyone in Brazil who day-traded futures for more than 300 days. 97% of them lost money, and only about 1% earned more than the minimum wage. That doesn’t mean Danya can’t try. It means he should start from an honest number, not a video, and only risk what he can afford to lose.

Details are a scammer’s tool

The same trap as with Linda works in scams. “A famous billionaire is giving away crypto” sounds dodgy. Add: “to celebrate a rocket launch, today only, send 1 coin and get 2 back”. Each detail makes the story more vivid and convincing, while the chance that it’s all true only drops. Scammers add specifics on purpose: a time, a reason, exact numbers. The more detailed and urgent the “unique offer”, the more carefully you check.

Hack: start from the base rate

Before any prediction about people, projects or chances, ask yourself: “How often does this happen in general?” Find at least a rough number. Then think about how reliable your story is: checked facts or someone’s stories and videos? And move away from the base rate carefully. If the base is 3% and the story is super inspiring, a sensible estimate is 5–10%, not “it’ll definitely work”. A good story can shift the base rate, but it can’t replace it.

Try it: base rates for your plans

Write down three of your plans or dreams. For each, find a base rate: how many people who try actually reach the goal? Danya wrote: living off trading (about 1% in the study), a channel with 100k followers (very few of those who start), a job in IT (much higher). He didn’t drop trading, but decided to practise on a demo account and learn programming at the same time. A base rate doesn’t forbid dreaming. It tells you where you need a plan B.

Check yourself

Steve is quiet and tidy. In the US, is he more likely a librarian or a farmer?
Correct answer: A farmer: there are 20+ times more of them. Yes. The description fits the stereotype, but there are so many farmers that the quiet, tidy ones still outnumber all librarians.
What’s more likely about Linda?
Correct answer: She’s a bank teller. Right. “Teller and feminist” is a part of all tellers. A part can’t be more likely than the whole, however well the story fits.
85% of cabs are green, 15% blue. A witness who’s right 80% of the time says “blue”. What’s the chance the cab was blue?
Correct answer: About 41%. Yes. Blue cabs are rare, so the witness’s mistakes about green cabs almost equal his correct calls about blue. Result: about 41%.
Danya wants to quit school and “trade for a living” after watching videos. What’s the honest starting point?
Correct answer: The base rate: in a big study, 97% of such traders lost money. Right. Honest base rate first, careful adjustment second. A sensible plan: practise on a demo account and don’t drop the main path.

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