Independence
A bell curve assembled out of coin flips
Drop six hundred balls through a board of pegs, each bouncing left or right at random, and they pile up in a shape that can be predicted precisely. Nothing coordinated them.
Getting pi by dropping needles on the floor
Throw a needle at a lined floor enough times, count how often it crosses a line, and pi falls out. There is no circle anywhere in the experiment.
Twenty-three people
A room needs 253 people before someone probably shares a birthday with you. It needs 23 before two of them probably share one with each other. The gap between those numbers is the whole problem.
A walk that always comes home, until it does not
Step left or right at random, forever, and the walk returns to where it started with certainty. On a grid it also returns. In space it does not, and about a third of walks leave and never come back.
The door that was not opened
Three doors, one prize, a host who opens a losing door and offers a swap. Switching wins two times in three, and the reason is not about doors — it is about what the host was allowed to do.
Named alongside it
The objects these essays reach for when they reach for this one.
ConvergenceBinomial distributionLimitNormal distributionPiAreaBayes' theoremBirthday problemBuffon's needleCollisionComplementary countingConditional probability