Probability test
Probability is where intuition fails most reliably. Streaks, coincidences, medical tests and game shows all have answers that feel wrong until you see why they’re right.
A fair coin lands heads five times in a row. What’s the chance the next flip is heads?
About this test
Every wrong answer here is a named mistake. You’ll find out after each question, and at the end you’ll see which mistakes caught you, with a course that starts from exactly those.
Questions people ask
What’s the most common probability mistake?
Ignoring the base rate, especially with medical tests: a positive result from an accurate test for a rare condition is often more likely to be a false alarm than a real case.
Is the Monty Hall problem really 2 in 3?
Yes. Your first pick is right 1 time in 3. The host always reveals an empty door, so switching wins whenever your first pick was wrong: 2 times in 3.
Does this need maths?
Only a little arithmetic. Every question can be reasoned out by picturing a crowd of people or a lot of coin flips.
Why do people find probability so counterintuitive?
Because our gut judges by how things look and feel, not by counting. A streak looks meaningful, a detailed story sounds likelier than a plain one, and two options feel like 50/50. Most of the questions here are places where counting the cases gives a different answer from the gut.
How long does the probability quiz take?
About nine minutes for the twenty questions. You see the answer and the reason after each one, so you learn as you go, and the result at the end shows which mistakes caught you.
Read more
- Base Rate Neglect: Why a Positive Test Often Isn’t What It Seems
- The Monty Hall Problem, Explained So It Finally Clicks
- The Gambler’s Fallacy: Is Tails Ever “Due”?
- The Birthday Paradox: Why 23 People Is Enough
- Relative vs Absolute Risk: What “50% Higher Risk” Really Means
- The Law of Large Numbers, Explained With Coin Flips
