Final answer:
In a cross between ppyyrr x ppyyrr, all offspring will be homozygous recessive for all traits; hence, the likelihood of just one recessive phenotype is 0% because they will display all recessive phenotypes.
Step-by-step explanation:
The cross described as ppyyrr x ppyyrr suggests that we are dealing with a trihybrid cross where all of the alleles are homozygous recessive. When both parents are homozygous recessive for a trait (pp, yy, and rr), all offspring will also be homozygous recessive and thus display the recessive phenotypes. No new combinations of alleles can form because the parents can only pass on one type of allele—the recessive one. This is an application of Mendelian genetics where the law of segregation states that allele pairs separate during gamete formation.
To answer the question of the likelihood that offspring will have one recessive phenotype: because both parents are homozygous recessive for all three traits, all of their offspring must also be homozygous recessive for all three traits. Therefore, the likelihood that the offspring will have just one recessive phenotype is 0%, because they will actually have all three recessive phenotypes.