Final answer:
The genotype for a homozygous dominant pea plant with round seeds is RR. Without more progeny, we cannot definitively determine if the parent plant with round seeds is RR or Rr based on only three offspring. If the plant is heterozygous (Rr), the probability that all three offspring will be round is 1/8.
Step-by-step explanation:
The genotype for a pea plant that is homozygous dominant for round seeds (R) is RR. When looking at the cross between a plant with wrinkled peas (genotype rr) and a plant with an unknown genotype that has round peas, if we end up with three progeny plants that all exhibit round peas, we cannot definitively tell if the unknown parent plant is homozygous dominant (RR) or heterozygous (Rr) based purely on this outcome. However, since all three offspring are round, there is a possibility that the parent is homozygous dominant, although more offspring would be needed to confirm this with greater certainty.
Assuming that the unknown round pea plant is heterozygous (Rr), to find the probability that a random sample of 3 progeny peas will all display the dominant (round) phenotype, we use Mendelian genetics. Each offspring has a 1/2 chance of being round if the unknown parent is heterozygous. Therefore, the probability that all three progeny are round is calculated as (1/2) x (1/2) x (1/2) = 1/8.