Final answer:
The round pea parent plant is heterozygous, and the probability of obtaining three round peas in a random sample of three progeny peas is 1/8.
Step-by-step explanation:
To determine if the round pea parent plant is homozygous dominant or heterozygous, we can use a Punnett square. The round pea parent is heterozygous because all three offspring have round peas. If the round pea parent plant is heterozygous, the probability of obtaining three round peas in a random sample of three progeny peas is 1/8.