Barred feather pattern is a z-linked dominant trait in chickens. what offspring would you expect from (a) the cross of a barred hen to a non-barred rooster? (b) the cross of an fl rooster from part (a) to one of his sisters?

Let the "barred" allele be caller B and the "non-white" allele b. Since chickens use chromosomes  and to determine sex, hens would have chromosomes , and roosters would have chromosomes . A Z-linked gene is represented as a superscript on the chromosome, for the dominant allele and for the ressesive allele.

A barred hen would have a copy of B on its Z chromosome, a non-barred rooster would have both copies of b on both Z chromosomes. Using Punnet squares to represent the crosses we get the following cases:

That is a ratio of two barred heterozygote roosters to two non-barred hens. Crossing them we get:

That is a ratio of one barred heterozygote rooster to one barred hen to one non-barred rooster to one non barred hen.