A brown-eyed man with a blue-eyed mother marries a brown-eyed woman with a blue-eyed father. What is the probability that their first child will be brown-eyed

This is based on my assumption that brown is dominant over blue.

Since both parent have parents who are homo_zygous recessive, this tells us that both parents will be hetero_zygous.

When you cross two hetero_zygous parents, it can produce these genotypic and phenotypic ratios:

Genotypic

BB : Bb : bb

1 : 2 : 1

Phenotypic

brown : blue

3 : 1

Therefore there is a 75% chance that they will produce a brown-eyed offspring.