This is the final exam for Thinking in Probabilities. It pulls together the whole course: the leap from possible to how probable, the outside view and the base rates everyone forgets, expected value and the ruin that can sink even a +EV bet, thinking in honest ranges instead of false-precision points, and the hard truth that a good decision and a good outcome are not the same thing. Take your time and reason each question through — several look easy until you notice the trap hiding in the numbers.
How this exam works
Read carefully — this exam is final. Each question appears one at a time. Once you submit an answer it is locked for good: there’s no going back, no retry, and no restart. Your score is hidden until the end, where you’ll see a pass/fail verdict. The pass mark is 70%. A few questions ask you to select all correct answers.
What is the cleanest distinction between possibility and probability?
Select an answer to continue.
Course Recap
Big picture
Thinking in probabilities, in one picture
- Thinking in Probabilities
- Possibility vs probability
- “Possible” is binary and near-useless; put a calibrated number on 0–1
- Base rates
- Take the outside view; the reference class’s frequency anchors your estimate
- Expected value
- EV = Σ(probability × payoff); mind variance and never risk ruin
- Thinking in ranges
- Points are false precision; give best/worst/base and 90% intervals
- Decision ≠ outcome
- Judge the process, not the result; beware resulting and hindsight bias
- Possibility vs probability
Key takeaways
Thinking in probabilities means refusing to stop at “it’s possible.” Almost everything is possible — the real question is how likely, expressed as a calibrated number (and convertible to odds). Start from the outside view: the base rate in the right reference class anchors any estimate, and ignoring it (Tom W., the cab problem) is the most common and costly mistake. Weigh choices by expected value — Σ(probability × payoff) — but never forget variance and the ruin problem: a +EV bet that can wipe you out isn’t worth it, because you only collect the long-run average if you survive. Quote your uncertainty as a range, not a false-precision point — best, worst, and base case, with a 90% interval — and remember the river that’s 4 feet deep on average still drowns you. Finally, in a world ruled by chance, a good decision is not the same as a good outcome: judge the process, resist resulting and hindsight bias, and give yourself enough trials for skill to separate from luck. Put a number on it — then judge the bet, not the result.