Final answer:
We can deduce the genotype of the round pea parent plant based on the phenotype of the offspring plants. If the round pea parent plant is heterozygous, the probability of all 3 progeny peas being round is 1/8.
Step-by-step explanation:
In pea plants, round peas (R) are dominant to wrinkled peas (r). If the offspring plants have round peas, we can deduce that the round pea parent plant is either homozygous dominant (RR) or heterozygous (Rr). However, if the offspring plants have wrinkled peas, we can conclude that the round pea parent plant is homozygous recessive (rr).
If the round pea parent plant is heterozygous (Rr), the probability that a random sample of 3 progeny peas will all be round is 1/8, or 0.125.
You cannot definitively determine if the unknown round pea parent plant is homozygous dominant (RR) or heterozygous (Rr) with only three round pea offspring. If the parent plant is heterozygous (Rr), the probability of all three progeny being round is 1/8.
In pea plants, round peas (R) are dominant to wrinkled peas (r). If you perform a test cross between a pea plant with wrinkled peas (genotype rr) and a plant of unknown genotype that has round peas (genotype either RR or Rr), you can determine the genotype of the unknown parent based on the offspring. When you end up with three offspring plants, all with round peas, you cannot definitively conclude whether the unknown round pea parent plant is homozygous dominant (RR) or heterozygous (Rr) just based on these results, as both crossings could produce round pea offspring. However, if we assume the round pea parent plant is heterozygous (Rr), the probability that a random sample of 3 progeny peas will all be round can be calculated using the Punnett square method. The probability that one round pea plant will be round when crossed with rr is 1/2. Therefore, the probability that all three will be round is (1/2)3 = 1/8.