# Common blood types are determined genetically by three alleles A, B, and O. (An allele is any of a group of possible mutational forms of a gene.) A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous. The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is P(p, q, r) = 2pq + 2pr + 2qr where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population. Use the fact that p + q + r = 1to show that the maximum proportion of heterozygous individuals in any population is 23.The maximum possible proportion of heterozygous individuals occurs when (p, q, r) = .

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Common blood types are determined genetically by three alleles A, B, and O. (An allele is any of a group of possible mutational forms of a gene.) A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous. The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is
P(p, q, r) = 2pq + 2pr + 2qr
where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population. Use the fact that
p + q + r = 1
to show that the maximum proportion of heterozygous individuals in any population is
2
3
.

The maximum possible proportion of heterozygous individuals occurs when
(p, q, r) =

.

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Step 1

Given:

Step 2

Solve p + q + r = 1 and put the value of this in above equation:

Step 3

Differentiate with respect to &ls...

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