The flower color in a plant is produced by the blending of pigments from two biosynthetic pathways involving three genes, which produce three enzymes that catalyze the steps involved in the pathways of pigment production. Flower colors produced by mixing pigments are yellow (Red + green) and purple (pink + blue). Pink, red, blue, and green flowers result from the production of single colored pigments, while white flowers result from the absence of pigment production. [Note: An uppercase letter indicates a dominant allele producing full enzymatic activity, and a lowercase letter indicates a recessive allele producing no functional enzyme]
A cross was done between pure-breeding plants that produced purple flowers with the one producing white flowers. If the F1 progeny was self-fertilized, determine the phenotypic ratio of the F2 progeny.