Ensemble Counts

Rare State Is a Count Ratio

A rare state is represented by a smaller finite weight. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Rare means fewer counted states

Weights 1 and 7 make probability 1/8 for the rare state.

1/8=181/8=\frac{1}{8}
Ensemble weight ledgerFinite state weights produce exact probabilities and expected counts.probprobcountcount

The rare expected count stays exact

In a population of 40, the rare expected count is 5.

40⋅18=540\cdot\frac{1}{8}=5
Ensemble weight ledgerFinite state weights produce exact probabilities and expected counts.probprobcountcount