Final answer:
The most likely genotypes of two parent pea plants with half smooth-seeded and half wrinkled-seeded offspring are both heterozygous (Rr). We cannot definitively determine if the round pea parent is RR or Rr from three round-pea offspring. A 16-square Punnett square is needed to analyze a cross between RrYY and rrYy or RrYY and rryy plants.
Step-by-step explanation:
Genetic Crosses in Pea Plants
In pea plants, round seed shape (R) is dominant to wrinkled seed shape (r). Based on the information provided, if two parent plants produce about half smooth-seeded offspring and half wrinkled-seeded offspring, the most likely genotype for both parents is Rr (heterozygous). A Punnett square of this cross would show equal probabilities for producing RR (homozygous dominant), Rr (heterozygous), and rr (homozygous recessive) offspring. However, the described offspring ratio suggests each parent is contributing an r allele, indicating the heterozygous nature of both.
When a test cross is performed between a wrinkled pea plant (rr) and a plant of unknown genotype with round peas, if all offspring have round peas, it is not sufficient to conclusively determine the unknown parent's genotype as either RR (homozygous dominant) or Rr (heterozygous). However, the probability of all progeny being round-pea if the round pea parent plant is heterozygous can be calculated. Each progeny has a 3/4 chance of displaying the round pea phenotype. The probability that all three progeny will exhibit round peas when the round pea parent is heterozygous is calculated as (3/4)^3.
For a cross between RrYY and rrYy or RrYY and rryy, the combination of Punnett squares for two traits requires a 16-square Punnett square to determine all possible genotypes and phenotypes.