In pigeons, a dominant allele C causes a checkered pattern in the feathers; its recessive allele c produces a plain pattern. Feather coloration is controlled by an independently assorting gene; the dominant allele B produces red feathers, and the recessive allele b produces brown feathers. Birds from a true-breeding checkered, red variety are crossed to birds from a true-breeding plain, brown variety.
(a) Predict the phenotype of their progeny.
(b) If these progeny are intercrossed, what phenotypes will appear in the F₂ and in what proportions?