Final answer:
The cross between two pea plants, each heterozygous for both tall height and round seeds (TtRr), results in various phenotypes due to the independent assortment of alleles. Observing only round-seeded offspring in a test cross does not conclusively indicate whether the round pea parent plant is homozygous dominant or heterozygous without further crosses or a larger progeny sample.
Step-by-step explanation:
Understanding Genetic Crosses and Phenotypes:
In the scenario presented, a cross between two pea plants, both heterozygous for tall height and round seeds (TtRr), the outcomes can be explained by independent assortment of alleles. This principle, one of Mendel's laws, describes how different genes independently separate from one another when reproductive cells develop. Each allele for a trait is passed on independently of the alleles for other traits resulting in a variety of genetic combinations. The observable characteristics, or phenotypes, of the offspring include tall with round seeds, tall with wrinkled seeds, short with round seeds, and short with wrinkled seeds. The phenotypes are the result of the underlying genotypes: TtRr, Ttrr, ttRr, and ttrr. For instance, the phenotype of a pea plant that is homozygous dominant (TT) for the tall trait is tall, and a heterozygous (Tt) pea plant will also be tall since the tall trait is dominant. The recessive traits, such as short height and wrinkled seeds, appear only when both alleles are recessive (tt or rr). When considering a test cross between a pea plant with wrinkled peas (rr) and a plant of unknown genotype with round peas, observing offspring all with round peas provides limited information regarding the round pea parent plant's genotype. It could either be homozygous dominant (RR), meaning all offspring will have round seeds, or heterozygous (Rr), where there is a 3:1 ratio expected in a large sample size. However, with only three offspring observed, it is not conclusive without further crosses. If the round pea parent plant is heterozygous (Rr), the probability of getting three progeny with round seeds from such a cross is (3/4)^3, since each offspring has a 3/4 chance of having round seeds when one parent is heterozygous.