Final answer:
The proportion of F2 offspring that are heterozygous for both gene pairs in a dihybrid cross between AA BB and aa bb is 1/4, following the independent assortment of alleles.
Step-by-step explanation:
The question involves a dihybrid cross of two organisms with the genotypes AA BB and aa bb. To find the proportion of offspring that are heterozygous for both gene pairs in the F2 generation, we first need to understand that the F1 generation will have all individuals with genotype Aa Bb, as these are the only gametes that the parents can produce.
In the F2 generation, which results from an F1 dihybrid cross (Aa Bb x Aa Bb), the ratio we are interested in is the chance of producing an offspring with Aa Bb genotype. Since the events are independent, we use the product rule to calculate this probability: 1/2 (for Aa) multiplied by 1/2 (for Bb), which equals 1/4. This means that the proportion of F2 offspring that are heterozygous for both gene pairs is 1/4.