An ensemble-state-probability cross-scan varies the macro-state across rows and reads off its probability, showing how the weights add up across microstates. The arithmetic is exact only for the stated states, probabilities, and rows in the ideal ensemble model. Real systems add finite samples, preparation bias, correlations, non-equilibrium effects, rate-estimation error, and measurement/source uncertainty.
One partition total normalizes three explicit state weights. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
State row 1 uses its weight over Z
State 0 has weight 4 over partition total 7, giving probability 4/7.
P0=74=74
State row 2 uses its weight over Z
State 1 has weight 2 over partition total 7, giving probability 2/7.
P1=72=72
State row 3 uses its weight over Z
State 2 has weight 1 over partition total 7, giving probability 1/7.
P2=71=71
The same partition total normalizes each state
The denominator stays seven across all rows. Larger explicit weight gives the larger probability.