Two brown-eyed parents can have a blue eyed child if both the parents had recessive blue-eye alleles. Alleles are basically alternative forms of a gene. They decide the physical appearance of genes of a child. In this case, eye color genes. There are are 2 types of alleles- dominant and recessive. Dominant alleles show up against recessive ones. If both parents were heterozygous- or had a hidden blue eyed recessive allele- then the child would have a possibility of getting 2 blue eyed alleles. Since recessive traits show up when they are the majority, the child would have a small chance of getting blue eyes.
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If each parent had one gene for brown eyes and one gene for blue eyes. This would result in brown eyes for the parents because the brown gene is dominant, and the blue gene is recessive. If their baby got the blue-eyed gene from both parents, then the baby would have blue eyes.
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They absolutely can. In our case, both my wife and I had a parent with blue eyes while she and I have brown eyes and one of our children was born with blue eyes. I am not the one to describe the genetics and dominant genes, etc.
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through grandparents are uncles, aunts etc.