Final answer:
The genotype of your parents would be Mother: BB, Father: Bb, as brown eye color is dominant. Both of your parents have the gene for brown eyes but since they are heterozygous it is possible for them to have a child with green eyes if the child inherits the green allele from both.
Step-by-step explanation:
If we are considering that brown eye color is dominant to blue eye color and knowing that your mother is homozygous for the trait while your father is heterozygous, and you have brown eyes, we can determine their genotypes. Because you have brown eyes and your mother is homozygous, she must carry two dominant alleles, therefore her genotype must be BB. Your father is heterozygous, which means he carries one dominant allele and one recessive, so his genotype would be Bb. Thus, the genotypes of your parents would be Mother: BB, Father: Bb.
The explanation for how a couple with brown eyes can produce a green-eyed child depends on the underlying gene interactions. Since eye color is determined by multiple genes, and not all of them follow simple Mendelian inheritance, both parents can carry hidden recessive alleles that may result in different eye colors in their offspring. If both parents are heterozygous, meaning they carry a gene for green eye color alongside a gene for brown, they could potentially have a green-eyed child if the child inherits the green allele from each parent.