Final answer:
The variety of offspring in the pea plant cross is due to the independent assortment of alleles. It is not possible to determine if the round seed parent plant is homozygous or heterozygous based solely on three round seed offspring. If heterozygous, the probability of all offspring being round seeded is 12.5%.
Step-by-step explanation:
The cross between two pea plants that are each heterozygous for both tall height and round seeds (TtRr) can be explained by the independent assortment of alleles. This principle, outlined by Gregor Mendel, states that different genes independently separate from one another when reproductive cells develop. The possibilities for height and seed shape are determined by the allele combinations from each parent, resulting in offspring with varying phenotypes such as tall with round seeds, tall with wrinkled seeds, short with round seeds, and short with wrinkled seeds.
To address the other part of the question regarding the genotype of the parent plant with round seeds, if all offspring from a cross with a rr wrinkled seed plant exhibit round seeds, it is impossible to definitively determine if the round seed parent plant is homozygous dominant (RR) or heterozygous (Rr) based on the sample of three offspring provided. A larger sample size would be needed to potentially reveal a rr offspring that would indicate a Rr genotype for the round seed parent.
If the round pea parent is indeed heterozygous, the probability of having three offspring all with round peas is 0.5 (probability of one offspring with round seeds) to the power of 3 (because there are three offspring), which equals 0.125 or 12.5%.