Three alleles (alternative versions of a gene) A, B, and O determine the four blood types A

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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.

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