Using the provided pedigree, determine the genotype of offspring 1 and the possible genotypes of offspring from a carrier woman and a hemophiliac man.

Offspring number 1 is a male, indicated by a square. The square is not shaded, which means he is a normal male according to the key.

Hemophilia is an X-linked recessive condition. $X^H$ is for non-hemophilia, $X^h$ is for hemophilia.
The mother of offspring 1 is a normal carrier female (circle with diagonal line), so her genotype is $X^H X^h$.
The father of offspring 1 is a normal male (unshaded square), so his genotype is $X^H Y$.

Offspring 1 is a male, so he inherits a $Y$ chromosome from his father. He inherits an X chromosome from his mother. Since he is normal, he must have inherited the $X^H$ allele from his mother.
Therefore, the genotype of offspring number 1 is $X^H Y$.

The genotype of offspring number 1 is $\boxed{X^H Y}$.

A carrier woman has genotype $X^H X^h$.
A hemophiliac man has genotype $X^h Y$.

The woman produces gametes $X^H$ and $X^h$.
The man produces gametes $X^h$ and $Y$.

From the Punnett square, the possible genotypes for sons are $X^H Y$ (normal son) and $X^h Y$ (hemophiliac son).

There are 4 possible offspring genotypes, and 1 of them is $X^h Y$ (hemophiliac son).
The probability is $\frac{1}{4}$.

The probability that the couple will have a son who is hemophiliac is $\boxed{\frac{1}{4}}$.