In a randomly mating laboratory population of Drosophila, 4 percent of the flies have black bodies (black is autosomal recessive, b), & 96 percent have brown bodies (normal color, B). If this population is assumed to be in Hardy-Weinberg Equilibrium. What are the allelic frequencies of B & b, & the genotypic frequencies of BB & Bb?

Hardy-Weinberg equilibrium: p^2+2pq+q^2=1 & p+q=1

where,

p = the freq of allele brown (B)
q = the freq of allele black (b)

P^2 = the freq of dominant homozygous (BB)

2pq = the freq of heterozygous (Bb)

q^2 = the freq of recessive homozygous (bb)
According to given problem,
the frequency of b = q = √frequency of bb = √0.04 = 0.2 & the frequency of B = p = (1-0.2) = 0.8
Allelic frequency of B = 0.8

Allelic frequency of b = 0.2

We can obtain the genotypic frequencies of BB & Bb based on allelic frequencies:

frequency of B = p = 0.8

frequency of b = q = 0.2

(p+q)=1
(p+q)^2 = (0.8+0.2)^2 = 1
p^2+2pq+q^2 = (0.8)^2+2(0.8)(0.2)+(0.2)^2

where,

p^2 = frequency of BB
2pq = frequency of Bb &

q^2 = frequency of bb
= 0.64+0.32+0.04 = 1
= BB Bb bb
Therefore, genotypic frequency of BB = 0.64 & genotypic frequency of Bb = 0.32