Exercise 58

Three alleles (alternative versions of a gene) A, B, and O determine the four blood types A (AA or AO), B (BB or BO), O (OO), and AB. The Hardy-Weinberg Law states that the proportion of individuals in a population who carry two different alleles is \(P = 2pq + 2pr + 2rq\) where p, q, and r are the proportions of A, B, and O in the population. Use the fact that \(p + q + r = 1\) to show that P is at most 2/3.