After determining that Jane is correct and that they cannot directly count carriers in the population, Amanda opened her notes from biology lecture. Dr. Jones had told them that the Hardy-Weinberg Equation, the mathematical expression of the Hardy-Weinberg Principle, can be stated as: (p+q)2 =1 or as (p2 + 2pq + q2 )= 1 "Jane, what the heck are p and q?" After consulting the text, Jane said, "I think I figured it out, p and q are allele frequencies. I think that in the case of complete dominance with two alleles, p represents the frequency of the dominant allele, and q represents the frequency of the recessive allele." "Right, so with only two alleles, then p + q = 1. I still don’t understand how this is helpful because we can’t determine p or q just by counting people in the population." "Amanda, is there another form of the equation, the one for genotypes?" "Yes, here it is. I think p2 represents the frequency of homozygous dominant genotype, 2pq represents the frequency of the heterozygous genotype, and q2 represents the frequency of homozygous recessive genotype." "That sounds right," said Jane. "And they add up to one because there are only three genotypes. "But what do we do now?" asked Amanda. "I don’t know," replied Jane. "But we might want to start by determining if we know any of these five values. We know q2 ." "Right!" said Amanda. "We could count people with the recessive phenotype in Corpus Christi and divide by the total number of people in Corpus Christi and we’d have q2 ." "Exactly!" said Jane. "And because we know q2 we can determine q. And if we know q, we can determine p. We are just about done with these questions!"

Once Jane and Amanda know the frequency of the homozygous recessive genotype (q2 ), how can they determine the frequency of the recessive allele (q)?