TwiddleLab / Courses / Math
Probability by Simulation
Flip a thousand coins, grow trees of chance and design a game that is actually fair.
Lessons
- Chance Is a Fraction (5 min): A probability is the share of the wheel that wins: 2 red slices of 10 is 2/10 = 0.2.
- Flip a Thousand Coins (7 min): The relative frequency is how often something happened: heads / flips.
- Counting the Outcomes (7 min): Two dice have 36 equally likely outcomes: a 6 by 6 grid. That grid is the sample space.
- And, Or: Overlaps Count Once (7 min): A and B is the overlap: the cells in both events.
- Independent or Not? (7 min): Events are independent when one tells you nothing about the other. A coin has no memory: after five tails, heads is still 1/2.
- Trees of Chance (7 min): A probability tree splits at every fork. A branch's thickness is its chance.
- At Least One: The Complement Trick (7 min): The complement of an event is everything else: P(not A) = 1 − P(A).
- Given That... (7 min): A clue removes every outcome that doesn't fit it. The cells left are the new whole.
- The Long-Run Average (7 min): The expected value is the long-run average per game: add up each outcome × its chance.
- Shapes of Randomness (7 min): A distribution says how often each result comes up. A histogram draws it as bars.
- Project: Design a Fair Game (8 min): A game is fair when the average prize equals the ticket: prize × chance = ticket.
Lessons are interactive and need JavaScript. Turn it on to play them.
