Answer:
a. The purple allele is lethal in the homozygous state
Explanation:
You cross a purple parrot with a true breeding (homozygous) white parrot and you get 1/2 purple parrots and 1/2 white parrots. This result can only happen if the purple parrot is heterozygous and the white parrot is homozygous recessive (if any of the parents had been homozygous dominant, 100% of the offspring would have had the dominant phenotype).
Then: Pp (purple) X pp (white) ---> 1/2 Pp, 1/2 pp
When you cross two purple parrots you get 1/3 white parrots and 2/3 purple parrots. The 2:1 phenotypic ratio is typical of a lethal allele in the homozygous state.
In a cross of two purple parrots: Pp
X Pp, one would expect the genotypic ratios 1 PP : 2 Pp : 1pp and the phenotypic ratios 3 Purple : 1 white.
But the PP genotype is lethal, so those individuals die and the only purple parrots we see are the heterozygous ones.