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Mathematical Modeling —— On Probability Model
You can try to establish a mathematical model with Markov chain.

Matlab code: (self-compiled, not copied)

TP =; % Set Initial State

Because i= 1: 10.

tp = tp * tp

end

Pi=now*tp% stable probability distribution, in which the first represents the probability of eating in public canteens and the second represents the probability of eating in private contracted canteens.

Running results:

The probability of eating in a public restaurant is 0.5556.

The probability of eating in the contracted restaurant is 0.4444.