Due to their sterility and lethality, AA and AA are unable to breed. Because all AA would perish, only heterozygotes would produce 2/3 Aa and 1/3 aa. The idea of random mating is not required.
A person having the genotype Aa can produce both A and a gametes. Given that this is a random process, the person will typically produce an equal quantity of each gamete. (For each gamete, the frequency is half.)
Homozygotes are people having the genotypes AA and aa (i.e., they have two copies of the same allele).
People who have the genotype Aa are heterozygotes (i.e., they have two different alleles at the A locus).
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