Final answer:
The pea plant with bumpy pods is homozygous recessive (bb), while the genotype of a plant with smooth pods could be either homozygous dominant (BB) or heterozygous (Bb). A Punnett square involving two heterozygous plants for a trait would have genotypes BB, Bb, or bb. When conducting a test cross between a rr plant and a plant with round peas, without a sufficiently large sample, one cannot determine if the round pea plant is homozygous dominant (RR) or heterozygous (Rr); if heterozygous, the probability of three round pea progenies would be 12.5%.
Step-by-step explanation:
To predict the genotype of a pea plant with bumpy pods when the allele for smooth pods is dominant to the allele for bumpy pods, one must understand Mendelian genetics. The plant with bumpy pods must be homozygous recessive, and its genotype would be bb. As for a plant with smooth pods, it could be either homozygous dominant (BB) or heterozygous (Bb), as the dominant allele for smooth pods would mask the presence of a recessive allele in a heterozygote. Therefore, without more information, such as the results from a test cross, one cannot definitively predict the genotype of a plant with smooth pods.
In the Punnett square analysis for a certain trait, if you're crossing two plants that are heterozygous, you'd be crossing Bb x Bb. The missing genotype in the Punnett square would be either BB, Bb, or bb, depending on the specific cross in question.
Performing a test cross between a pea plant with wrinkled peas (genotype rr) and a plant of unknown genotype that produces round peas can help determine the unknown genotype. If all resulting offspring have round peas, the unknown genotype might initially seem to be homozygous dominant (RR), but you cannot conclude this with certainty unless the sample size is larger. If the round pea parent plant is heterozygous (Rr), the probability that a random sample of three progeny peas will all be round is 0.5 * 0.5 * 0.5, which equals 0.125 or 12.5%.