Answer:
The woman's genotype - Bb
The man's genotype - bb
Chances of having a child with blue eyes - 50%
Chances of having a child with brown eyes - 50%
Explanation:
Many of our traits are determined by our genetics. We inherit genetic information from both of our parents. From each of them, we get one copy of a gene that determines a certain trait. These gene copies are called alleles.
The dominant allele is the one that masks the effect of the other type of allele, called the recessive allele. This means that a person needs to have only one dominant allele in order for its effect to be expressed. In order for the effect of the recessive allele to be expressed, the person needs to have two recessive alleles.
If a man has blue eyes, which is a recessive trait, he needs to have two recessive alleles (bb). This is why the genotype of the man is bb.
If his child has blue eyes, this means that its genotype is bb as well. The mother's eyes are brown, which means that she needs to have at least one recessive allele. Based on this, we can conclude that her genotype is Bb.
Since the mother has one dominant allele, this means that her children could have brown eyes as well. This is what the Punnett square would look like:
B b
b Bb bb
b Bb bb
Two out of four children would have brown eyes, and the other two would have blue eyes. This means that their chances of them having a child with blue eyes are 50%. The chances of them having a child with brown eyes are the same.