Final answer:
Lucia's seeds, which are wrinkled, must be homozygous recessive with a genotype rr. When a test cross yields only round seeds it's not enough information to determine if the round seed plant is homozygous or heterozygous. If the plant is heterozygous, the probability of all offspring being round is (3/4)^3.
Step-by-step explanation:
In pea plants, a round seed texture is denoted by the dominant allele R, while a wrinkled seed texture is represented by the recessive allele r. Lucia's seeds are wrinkled, indicating they are in the homozygous recessive condition with a genotype of rr. This follows Mendelian genetics principles, where two recessive alleles are required to express a recessive trait.
When discussing a test cross involving a plant of unknown genotype with round seeds against a plant with wrinkled seeds (genotype rr), and all offspring have round seeds, we cannot conclusively determine the genotype of the round seed plant solely based on three offspring. A larger sample is needed. However, if we assume the round seed parent is heterozygous (Rr), the probability of all three offspring having round seeds would be (3/4)^3, as each offspring has a 3 in 4 chance of being round if one parent is heterozygous. The Punnett square analysis supports these probability calculations.