Part 1) Brown eyes are caused by the iris having a higher concentration of melanin, so they are far more common in people whose ancestors live in a warm climate since melanin protects the eyes with the brighter sunlight. Lighter color eyes are more common in colder climates.
Part 2) The allele for blue eyes is also recessive while brown is dominant. So in order for a child to have blue eyes passed down to them the parent each have to provide a blue allele. So if two parents each have one brown and one blue allele then a child would have a 25% chance of having blue eyes and a 75% chance of having brown eyes. It is a bit more complicated than that as there is more than just one allele and mutations sometimes can happen including some children getting one blue eye and one brown eye. It is cool stuff!
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