A population has a gene with 2 alleles, G and g. The frequency of the G allele is 0.8. The frequency of the g allele is 0.2. This is all that you know. What is the frequency of the GG genotype?

Answer: The frequency of GG is 0.64

Explanation: using Hardy-weinberg equation

g^2 + 2Gg + G^2 = 1 ... (1)

And the sum of the alleles at the locus must be 1.

Therefore:

G + g = 1 ... (2)

Since

G=0.8

g = 0.2

G^2 = GG (Homozygous G gene)

g^2 = gg (Homozygous g gene)

Using equation 1

GG + (2*0.8*0.2) + gg = 1

Therefore

GG + 0.32 + gg = 1

GG + gg = 0.68 ... (3)

Solving equation 2

G + g = 1

g = 1 - G

Square both side

g^2 = (1 - G) ^2 ... 4

Where g^2 = gg

Therefore gg = (1 - G) ^2 ... (5)

Substitute equation 5 into equation 3

GG + (1 - G) ^2 = 0.68

Therefore

GG = 0.68 - (1 - G) ^2

GG = 0.68 - (1 - 0.8) ^2

GG = 0.68 - 0.04

GG = 0.64