In the datura plant, purple flower color is controlled by a dominant allele P. White flowers are found in plants homozygous for the recessive allele p. Suppose that a purple-flowered datura plant with an unknown genotype is self-fertilized and that its progeny are 28 purple-flowered plants and 10 white-flowered plants. Use the results of the self-fertilization to determine the genotype of the original purple-flowered plant. If one of the purple-flowered progeny plants is selected at random and self-fertilized, what is the probability it will breed true

The genotypes PP and Pp determine purple flowers while pp determines white flowers.

A purple-flowered P_ (PP or Pp) plant is self-fertilized and it produces the progeny:

28 P_ purple 10 pp white

The only way to obtain plants with white flower in the progeny is if both parental plants have a recessive p allele, so the genotype of the original purple-flowered plant is Pp.

The original cross then was Pp x Pp. The expected offspring (from Punnett Square) is 1/4 PP, 1/2 Pp and 1/4 pp. If we only consider the purple-flowered offspring, the proportion of genotypes is 1/3 PP and 2/3 Pp. To breed true, the individuals must produce only homozygous progeny. Only the PP individuals will breed true, so the probability is 1/3.