Final answer:
To determine if a plant is homozygous or heterozygous, perform a test cross with a homozygous recessive plant. The results will show if the plant is homozygous dominant or heterozygous. In heterozygous cases, calculate the probability of a trait appearing in a sample using Mendelian ratios.
Step-by-step explanation:
To determine whether a plant is homozygous or heterozygous, you can perform a test cross. This involves crossing the plant in question, which exhibits the dominant phenotype, with a plant that is homozygous recessive for that trait. If all offspring express the dominant trait, then the test plant is homozygous dominant.
If there is a 1:1 ratio of dominant to recessive phenotype among the offspring, the test plant is heterozygous. Considering a case with pea plants, if the round pea parent plant is heterozygous (Rr), and assuming round (R) is dominant over wrinkled (r), there is a 3:1 ratio of round to wrinkled offspring.
If a random sample of three progeny peas is taken, the probability that all three will be round (dominant phenotype) is calculated by the probability of each being round (3/4) raised to the power of the sample size (3), which is (3/4) ^3.