Brown eyes is dominant to green eyes. Blue eyes is recessive to all eyes. Kate has green eyes (Her mother had brown eyes and her father had blue eyes). She marries Tom, who has brown eyes (his mother had blue eyes and his father had brown eyes). What are the odds that their child will have blue eyes?

 To solve this problem, we need to determine the genotypes of Kate and Tom.

Kate has green eyes, which is recessive to brown but dominant to blue. Since her father had blue eyes and blue is recessive, he must have had the genotype bb (two recessive alleles). Her mother had brown eyes and Kate ended up with green, so her mother must have had at least one gene for green eyes. Since green is not as dominant as brown, Kate's mother's genotype must have included the green allele (let's use G for brown, g for green, and b for blue). Since the phenotype of Kate's mother was brown, she could have been either Gg or GG. But since Kate exhibits green eyes, her mother must have been Gg. Therefore, Kate's genotype must be gb.

Tom has brown eyes and since blue is recessive and his mother had blue eyes, she must have had the genotype bb. So, Tom got a b allele from his mother. For him to have brown eyes, his father must be either Gb or GG. But we know Tom carries a blue allele because of his mother. Therefore, his genotype must be Gb.

Now that we have their genotypes, we can draw a Punnett Square for Kate's gb and Tom's Gb to determine the possible genotypes for their children:

G b --------------------- g | Gg | gb | --------------------- b | Gb | bb | ---------------------

Kate and Tom's children could therefore have the following genotypes: Gg (Green eyes, because green is recessive to brown), gb (Green eyes since there is no dominant brown allele), Gb (Brown eyes), and bb (Blue eyes).

There is only one way for them to have a child with blue eyes (bb), out of four possibilities. The odds for their child having blue eyes is therefore 1 in 4, or 25%.