Answer: The genotype for the parent organism whose genotype is unknown is Ff.
Explanation: Let (F) represent the allele for purple which is dominant over (f) and (f) represent the allele for white.
The parent organism whose genotype is unknown is heterozygous for purple colour (Ff).
A cross between Ff and ff will produce four offsprings: two of which are Ff (heterozygous for purple colour) and two are ff (white).
Ff x ff = Ff, Ff, ff and ff.
Since (F) is dominant over (f), (Ff) will manifest as purple while (ff) will manifest as white. Therefore, half of the offsprings are purple while the other half are white.
See the attached punnet square for more information