There is a population of alien kitties, species Cattus really-defty, that live on the planet Scratch. Their genomes and biology are amazingly identical to the genomes and biology of earth cats. Consider a di-hybrid cross, where the first locus has alleles A and a, and second locus has alleles B and b. Each additional copy of either an A or B allele in the two-locus genotype increases the adroitness of the cat. Adroitness is measured by the Liverpool-LI Diagnostic Juggling Measurement Instrument (LLDJMI). There are five categories: 0 = Minimally adroit (has difficulty walking across the back lawn);
1 = Somewhat adroit (can walk, but has difficulty catching mice);
2 = Adroit (can catch mice, birds, small animals easily);
3 = Very adroit (can join the circus and get a high-paying job).
4 = Extremely adroit (usually works as a Formula I race-car driver).

As an example, an alien cat with a two-locus genotype of AAbb is categorized as the Adroit phenotype (Category = 2), since there is two copies of A and zero copies of B, adding to a score of 2 for the LLDJMI. Similarly, an alien cat with a two-locus genotype of AaBB has a Very adroit phenotype (Category = 3) (one copy of A + two copies of B = three copies total of A or B).

In the following mating: AaBb x AaBb, what is the expected proportion of offspring that will be Adroit?