Give the two states equal weights and their normalized probabilities come out equal, so each holds half the population. That 50/50 split is exact only for the stated weights, the two listed states, fixed temperature/model, and equilibrium sampling. Real systems add preparation bias, finite sampling, calibration, degeneracy, and uncertainty.
Energy labels alone do not determine the shown population. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Equal explicit weights give equal populations
With equal weights, the upper fraction is one half.