Final answer:
The most likely genotypes of the parents are F^RF^R and F^WF^R.
Step-by-step explanation:
The most likely genotypes of the parents are FRFR and FWFR. This is because in the offspring, there are two different genotypes observed: FRFR and FWFR. This suggests that the parents have different but related genotypes, with one parent being homozygous for the red color allele (FRFR) and the other parent being heterozygous for the white and red color alleles (FWFR).