Probability simulations, Part I

Interactive simulations for the STA102 slides. Press a button and thousands of random experiments run in your browser; watch the long-run frequencies settle on the values the slides prove.

Each page names the slides it belongs to. Everything is self-contained: no accounts, no downloads, no tracking.

Why should anyone care about chance?

The opening deck: long-run frequency, order out of chaos, and four puzzles.

The long run

Toss a coin, roll a die or bet on red thousands of times and watch the running fraction settle.

Also: Probability and what happens when you learn something

Order out of chaos

A Galton board, and the averages of several dice turning into a bell curve.

Estimating π with darts

Throw random darts at a square and count how many land inside the quarter circle.

Random walks

Step left or right at random. How far do you get after n steps? About √n.

The birthday problem

Fill a room with random birthdays. How often do two people share one — and how often does someone share yours?

Also: Probability and what happens when you learn something

Monty Hall

Play the game yourself, then simulate thousands of games with 3 to 100 doors.

Also: Probability and what happens when you learn something

The positive test

A 95%-accurate test for a rare disease, drawn as a town of 10,000 people.

Also: Probability and what happens when you learn something

De Méré and Galileo

The Chevalier's two bets, and why three dice total 10 slightly more often than 9.

Also: Probability and what happens when you learn something

Sets: the language of events

Sample spaces, events and set operations on the two-dice grid.

Events on the two-dice grid

Pick events A and B, see unions, intersections and complements, then roll to check.

Also: Probability and what happens when you learn something

Counting

Permutations, combinations and the numbers behind cards and lotteries.

Poker hands and card puzzles

Deal thousands of hands and shuffle thousands of decks: full houses, flushes and the first ace.

Also: Probability and what happens when you learn something

The lottery

Pick six numbers from 49 and play for as many weeks as you like.

Probability and what happens when you learn something

Axioms, equally likely outcomes, conditioning and total probability.

Conditioning by throwing runs away

Peek at a die, hear the news about two coin tosses, and open Bertrand's boxes.

Also: Why should anyone care about chance?

Simpson's paradox

Why treatment A wins for small stones and for large stones, but loses overall.

Additional material

The matching problem, the gambler's ruin and non-transitive dice.

The matching problem

Hand phones back at random. Nobody gets their own about 37% of the time, whatever the class size.

Also: Probability and what happens when you learn something

The gambler's ruin

Bet one unit at a time until you hit a target or go broke; bold play; deuce; a race to roll a six.

Also: Probability and what happens when you learn something

Non-transitive dice

Four dice that beat each other in a circle. Pick one; I'll pick the one that beats it.