Probability Puzzles and Paradoxes
Sharpen your reasoning with famous puzzles, then settle every argument by counting or simulating
A taste of a lesson
In Monty Hall, after one goat door opens, there are two doors left. Isn't it just 50/50?
It feels that way, but the host's choice is not random. Count the cases. Your first pick is the car one time in three; then switching loses. Two times in three your first pick is a goat; the host must open the other goat door, so the remaining door has the car, and switching wins. So switching wins 2/3 of the time. The two doors are not equally likely because the host used knowledge. Test it: deal three cards, one ace, play the host 30 times, and count how often switching wins.
Written by the teacher as an example. In your lesson the tutor answers your own questions, and like any AI it can be wrong.
What you will be able to do
- Resolve classic probability puzzles by counting or simulation
- Explain how wording and information processes change answers
- Recognise the prosecutor's fallacy and base rate neglect in real cases
- Spot regression to the mean in data and evaluations
- Explain why expected value alone can mislead decisions
Lesson plan
- 1 Monty Hall Resolve the Monty Hall problem and see why the host's rule matters. Start
- 2 Birthdays and coincidences Understand why coincidences are more common than intuition says. Start
- 3 Boxes and children Work through Bertrand's box and the boy or girl problem. Start
- 4 Fallacies in the courtroom and clinic Recognise the prosecutor's fallacy and base rate neglect. Start
- 5 Regression to the mean Spot regression to the mean in data and evaluations. Start
- 6 Streaks and infinite games Discuss the gambler's fallacy, hot hands and the St Petersburg paradox. Start
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About this tutor
A tutor for curious learners at any level who enjoy puzzles and want sharper probabilistic reasoning. You will work through classics such as the Monty Hall problem, the birthday problem, Bertrand's box, the boy or girl problem, the prosecutor's fallacy, regression to the mean and the St Petersburg paradox. For each, you first commit to an answer, then resolve it by careful counting, a frequency tree or a quick simulation, and finally connect it to a real situation in data work, medicine, law or everyday life. Wording matters in every puzzle, and the tutor treats that as part of the lesson.
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About the teacher
Probability for machine learning, plus forecasting and anomaly detection
9 tutors 361 lessons taught Sample
I teach probability the way machine learning uses it: random variables, likelihood, entropy and simulation. I also teach two applied areas where probability matters every day: time series forecasting and anomaly detection. My work background is in monitoring and forecasting for operational systems, where wrong alarms and missed incidents both have a cost. I teach through small simulations, coin and...
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