Matpic
mathematics, in pictures
Ladder

Expectation — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. 10 → 11.201 → 21.502 → 323 → 434 → 565 → 614.70 draws expected in all6 kinds, and the last is the expensive onethe waits are 6/6 + 6/5 + 6/4 + 6/3 + 6/2 + 6/1 = 14.70 drawsthe last one alone costs 6 draws on average, which is why the total grows faster than the number of kinds

    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.

    rung 1 · probability

All ladders