Holding ensemble weights fixed while population changes separates probability from expected count. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Twenty particles gives five in the moving state
The state weights stay 2 and 6, so the moving probability is 1/4. A population of 20 gives expected moving count 5.
20⋅41=5
Forty particles gives the ten-count audit row
With the same probability 1/4, doubling population to 40 doubles the expected moving count to 10.
40⋅41=10
Sixty particles keeps the fraction and raises the count
At population 60, the same one-fourth probability gives expected moving count 15. The scan separates probability from population size.