Answer:
Option A
Percent of the population that has skin pigment but also carries the recessive allele is [tex]21\\[/tex] percent
Explanation:
As per hardy-weinberg equation,
[tex]p^2+q^2+2pq = 1\\[/tex]------------- Eq(A)
where
[tex]p^2= \\[/tex]frequency of the homozygous genotype (dominant)
[tex]q^2= \\[/tex]frequency of the homozygous genotype (recessive)
[tex]pq= \\[/tex]frequency of the heterozygous genotype (recessive)
Also, sum of the allele frequencies at the locus is equal to one.
Thus, [tex]p + q = 1\\[/tex] ------------- Eq(B)
Here frequency of recessive allele i.e [tex]q = 30\\[/tex]%
Substituting this in equation B, we get
[tex]p + 0.3 = 1\\p = 1-0.3\\p= 0.7\\[/tex]
frequency of dominant allele i.e [tex]q = 70\\[/tex]%
Substituting the value of frequency of both dominant and recessive allele in equation A, we get
[tex](0.3^2) + (0.7^2) + 2pq = 1\\pq = \frac{1-0.3^2-0.7^2}{2} \\pq = \frac{0.42}{2} \\pq = 0.21\\[/tex]
Thus, percent of the population that has skin pigment but also carries the recessive allele is [tex]21\\[/tex] percent
