What fraction of the children should be homozygous smooth

what fraction of the children should be homozygous smooth?

Incomplete. You need to supply much more information.

To determine the fraction of children that should be homozygous smooth, we need to know the parental genotypes and the mode of inheritance.

If we assume that the trait being discussed is influenced by a single gene with two alleles (let's say S for smooth and s for rough), and if the parents are both heterozygous (Ss), then we can use the Punnett square to calculate the expected genotypes of their children.

The Punnett square for this scenario would look like:

S s
--------------------
S | SS | Ss |
--------------------
s | Ss | ss |
--------------------

From the Punnett square, we can see that there is a 1/4 (or 0.25) probability of having children who are homozygous smooth (SS).

To determine the fraction of children that should be homozygous smooth, we need some background information. Are we referring to a specific genetic trait or population?