Question

If you know that a population is 75% the dominant phenotype and 25% is the recessive phenotype, can you determine approximately how many of the dominant phenotype are homozygous dominant and how many are heterozygous dominant? Try this mathematically

Answer 1

If dominant allele = p, and recessive allele = q,
and p+q = 1, then:
${(p + q)}^{2} = {p}^{2} + 2pq + {q}^{2} \\ where \: {p}^{2} \: is \: homozygous \: domin \\ {q}^{2} \: is \: homozygous \: recessive \\ and \: 2pq = heterozygous$
So if 75% have the p, then p^2 = homozygous dominant
${p}^{2} = {(.75)}^{2} = .5625$
And if the other 25% have the q, the q^2 = homozygous recessive
${q}^{2} = {(.25)}^{2} = .0625$
Now those remaining MUST be the heterozygous, thus 2pq are those:
2pq = 2(.75)(.25) = .375

Therefore homozygous dominant are 56.3% and heterozygous are 37.5%