This is in reality a biology question given a lot of biology related information is not given in the problem.
However, I will provide the answer by making biology-related assumptions.
1. The genotype of the purple-flowered progeny is Pp
2. The purple-flower phenotype is recessive.
If self fertilized, both "parents" have genotype Pp
The punnett square is as follows:
P p
P PP Pp
p Pp pp
Since purple-flowers are recessive, only PP will come out purple, hence the probability is 1/4.
