Sample space
Named by 4 essays across one field — each of them below, with the objects they name alongside it.
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.
Nobody gets their own hat
Hand back a pile of hats at random and ask for the chance that not one person gets their own. The answer barely moves as the crowd grows — it is a third and a bit at four people, and a third and a bit at four thousand.
How long until every one turns up
Draw at random from six equally likely kinds until all six have appeared. The wait is not six draws, and it is not sixty; it is fourteen point seven, and the number is a harmonic sum wearing a hat.
The rule that forgets where it came from
A walk between a few states, with the next step decided by the current one and nothing else. Run it long enough and the starting point stops mattering — but only when two conditions hold, and both of them have a picture in which they fail.
Named alongside it
The objects these essays reach for when they reach for this one.
ApproximationCounting argumentRecurrenceAlternating seriesAreaBayes' theoremCollisionComplementary countingConditional probabilityConvergenceConvergence rateCounting two ways