Multiplying a probability by the population gives the expected count in each state, so a larger population scales every expected count proportionally. With population 40 and probabilities 1/4 and 3/4, the expected counts are 40 times 1/4 = 10 and 40 times 3/4 = 30 exactly for the stated toy count ledger; real particle counts fluctuate, depend on sampling windows, state assignment, drift, and measurement uncertainty.
Expected counts are checked integer products of population and probability. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
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Choose a finite population
A population of 40 makes both expected counts integers.