Final answer:
In a cross of pea plants, the round seed shape (R) is dominant to wrinkled (r). Without more data, we can't be sure if a round-seeded parent is homozygous dominant or heterozygous based on just three round-seeded offspring. If heterozygous, there is a 27/64 probability of three round-seeded offspring. F1 hybrids would be round-seeded, and F2 progeny would have a typical Mendelian 3:1 ratio in a monohybrid cross.
Step-by-step explanation:
In pea plants, the round seed shape (R) is dominant over the wrinkled seed shape (r). When a test cross is conducted between a plant with wrinkled seeds (genotype rr) and a plant with round seeds of unknown genotype, and all offspring have round seeds, we cannot definitively determine if the round-seeded parent is homozygous dominant (RR) or heterozygous (Rr) based on these three offspring alone. More offspring would increase the reliability of the determination. However, if we assume that the round-seeded parent is heterozygous (Rr), the probability of obtaining three round-seeded offspring from this parent crossed with a wrinkled-seeded plant (rr) is (3/4) X (3/4) X (3/4) = 27/64, because each offspring has a 3/4 chance of being round-seeded due to the dominance of the R allele.
The trait of F1 hybrids in a cross between a round-seeded plant and a wrinkled-seeded plant would be round seeds (Rr), as the dominant allele R expresses the round seed phenotype. When these F1 hybrids are self-crossed to produce F2 progeny, a typical Mendelian ratio of 3:1 for dominant to recessive traits would be expected, resulting in approximately three-quarters of the progeny with round seeds and one-quarter with wrinkled seeds. The name of this cross is a monohybrid cross as it involves a single trait.