Ensemble weights turn into probabilities by dividing each weight by the total, so no random draw is needed to compute the distribution. With weights 2 and 6 the total is 8, giving probabilities 2/8 = 1/4 and 6/8 = 3/4 exactly for the stated toy ensemble ledger; real ensembles have finite-sample noise, hidden states, non-equilibrium bias, counting limits, and measurement uncertainty.
Finite state weights make exact probabilities without sampling. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Count state weights first
The two state weights are 2 and 6, so the total weight is 8.
2+6=8
Weights become exact probabilities
The probabilities are 1/4 and 3/4; no random draw is used.