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From what I've read, it seems that they select a random sample of 50,000 - 55,000 winners from the pool of applicants worldwide. But from the statistics I've seen, the distribution is not uniformly random. My next guess is that they select a random sample of 50,000 - 55,000 winners, and then apply rejection sampling so that no country has more than 7% winners. My guess is probably not correct. What is the precise algorithm/procedure the U.S. States Department uses to arrive at the final selection?

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Every year the U.S States Department randomly selected 50,000 applicants for the Green Visa lottery program. All applicants are selected randomly as a whole, for the number of visas allocated for that region, but with the limitation that no single country may receive more than 7% of the total diversity visas. That is the maximum number of applicants per country that can get a green visa is not more than 3,500.

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