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Probability Puzzles Tutor

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Learn probability through questions, not lectures.

The Open buttons send the prompt text as currently shown below to that site only when you click. Fill in the placeholders first.

Tutor me in probability using questions. Topic: [PROBABILITY_TOPIC]. My level: [MY_LEVEL]. Time: [MINUTES] minutes.

Rules: give me one problem at a time; wait for my answer; if I am wrong, do not reveal the answer; ask a question that exposes my mistake, then let me retry; only after two tries show a worked solution. Start easy and increase difficulty when I answer two in a row correctly.

Plan the session: a warm-up with coins and dice; conditional probability with a medical-test style problem expressed as natural frequencies (out of 1,000 people); independence versus mutual exclusivity; the birthday problem with a simulation I can run in code; expected value with a decision; and one misleading intuition such as the gambler's fallacy.
After each problem add a line "Why people get this wrong". At the end give a summary table of problems, my attempts, and the concept to revisit, and a 10-line Python simulation to check one answer by experiment. Do not use jargon without defining it.

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Puzzle: Two dice are rolled. What is the probability that the sum is 8?
Hint 1: How many outcomes are there in total? (36)
Hint 2: List the pairs that add to 8: (2,6), (3,5), (4,4), (5,3), (6,2).
Attempt: 5/36 ≈ 0.139.
Check: you counted (4,4) once, correct.
Extension: probability of at least one six = 1 - (5/6)^2 = 11/36.
Misconception to watch: thinking each sum is equally likely.
Practice: three more puzzles, answers hidden until you try.
Follow-up: explain in your own words why the pair (2,6) and (6,2) count as different outcomes, and I will check your reasoning.

• probability-tutor