Final answer:
To determine if an F2 round seed pea plant is homozygous dominant or heterozygous, a test cross with a homozygous recessive (wrinkled seed) plant is performed. If the parent is heterozygous, the probability of all three progeny being round is 12.5%.
Step-by-step explanation:
In pea plants, traits are determined by dominant and recessive alleles, where round peas (R) are dominant to wrinkled peas (r). To determine the genotype of an F2 plant with round seeds from a monohybrid cross, one would perform a test cross with a pea plant of known genotype. Specifically, the cross should be with a plant with wrinkled seeds (rr), which is always homozygous recessive.
If the unknown plant was homozygous dominant (RR), all offspring would have round seeds. However, if the plant is heterozygous (Rr), there is a 50% chance for each offspring to have round seeds. Therefore, observing all round seeds in three offspring does not definitively determine the genotype of the round pea parent plant as homozygous dominant or heterozygous. We need a larger sample size to increase confidence in our determination. If we assume the round pea parent plant is heterozygous, the probability that a random sample of three progeny peas will all be round is ½ x ½ x ½ = ⅔ or 12.5%.