Answer:
a. When a man with blue eyes (genotype: bb) marries a brown-eyed woman (genotype: Bb), whose mother had blue eyes (genotype: bb), the possible genotypes of their offspring are Bb (brown-eyed) and bb (blue-eyed). The Punnett square for this cross would be:
```
b b
B Bb Bb
b bb bb
```
In this scenario, 50% of the children would be expected to have blue eyes (genotype: bb).
b. If a brown-eyed man (genotype: Bb) marries a blue-eyed woman (genotype: bb) and their first child is blue-eyed, the possible genotypes of the man would be Bb or bb. Since the child has blue eyes, the man must have the genotype bb to pass on the recessive allele for blue eyes. Therefore, the man's genotype is bb.