For the figure 57.5% at the end of Example 1.3-3 to be true, should we assume that the citizens are migrating independently?

Example 1.3-3

We revisit Example in Section 1.1. Doing simple calculations or using software, we get

Thus, the probability that a randomly chosen citizen will live in area 0 at time t = 3 is 0.575. However, it would be a mistake to think that this means that in the third year 57.5% of people will live in area 0. The process is random, and the percentage mentioned is also random. The figure 57.5% is the expected value of the percentage of citizens of area 0 in the year mentioned. Let us show it rigorously.