Final answer:
The correct genotypic proportions of offspring from a self-cross of a hybrid AaBbCeDd are (D) 8:4:16:81, determined by using probability methods and understanding independent assortment and dominance.
Step-by-step explanation:
The student's question pertains to predicting the genotypic proportions resulting from a self-cross of a hybrid organism with the genotype AaBbCeDd. Using probability methods and understanding of independent assortment and dominance, we can determine the expected proportions of certain genotypes in the offspring when this hybrid is selfed.
Each gene pair (Aa, Bb, Ce, Dd) will assort independently, and we can apply the product rule to calculate the probabilities for the offspring genotypes. The product rule states that the probability of two independent events occurring together is the product of their individual probabilities. Since the question is asking for proportions involving both dominant and recessive alleles, the calculations are a bit more intricate than just using the 9:3:3:1 phenotypic ratio.
For the genotype AABBCCDd, you need individuals to be homozygous dominant for A, B, and C and either homozygous or heterozygous for D. The proportion of offspring with this genotype would be (1/4 × 1/4 × 3/4 × 3/4), following the sum and product rules. Similar calculations apply to the other genotypes, and once all proportions are calculated and simplified, the correct genotypic proportions, corresponding to (D) 8:4:16:81, are obtained.