I quote this question from "All of Statistics":
Suppose a gene can be type A or type a. There are three types of people (called genotypes): AA, Aa, and aa. Let (p, q, r) denote the fraction of people of each genotype. We assume that everyone contributes one of their two copies of the gene at random to their children. We also assume that mates are selected at random. The latter is not realistic however, it is often reasonable to assume that you do not choose your mate based on whether they are AA, Aa, or aa. (This would be false if the gene was for eye color and if people chose mates based on eye color.) Imagine if we pooled everyone’s genes together. The proportion of A genes is P = p + (q/2) and the proportion of a genes is Q = r + (q/2). A child is AA with probability P^2, aA with probability 2PQ, and aa with probability Q^2. Thus, the fraction of A genes in this generation is P^2 + PQ
This is probably a basic question. I'm asking: why is $A = P^2 + PQ$ and not $P^2 + 2PQ$?