Final answer:
The student has brown eyes with one parent being homozygous (BB) and the other heterozygous (Bb). They inherited the brown (B) allele from both parents but also a recessive blue (b) allele from the heterozygous parent, enabling them to have a child with blue eyes (bb). Option b.
Step-by-step explanation:
In humans, eye color is an example of complex inheritance, where multiple genes and alleles are involved. The brown eye color allele (B) is dominant over the blue eye color allele (b).
If a child has blue eyes (bb), at least one parent must carry the blue allele.
Since you have brown eyes and one of your parents is heterozygous (Bb), for you to have a child with blue eyes, your other parent cannot be homozygous for the brown allele (BB), because in that case you could only carry brown alleles and therefore could not pass on a blue allele to your child.
The correct answer considering your brown eyes and having a child with blue eyes would be:
Mother: BB (homozygous brown)
Father: Bb (heterozygous brown)
You must have inherited one brown allele from each parent to have brown eyes, but you have inherited a recessive blue allele from your father, making your genotype Bb.
Your partner must also have blue eyes (bb) for your child to have a blue eye color, indicating a genotype of bb for the child.
So option b is correct.