I am so confused I have provided the answers to this problem

I am so confused. I have provided the answers to this problem, I just don\'t know what formula they used in (2b) to calculate p and q, which is different from the formula I have been using. Thanks

2a) Fur color in prairie mice is controlled by a single locus, two alleles system. BB individuals are black, BW individuals are gray and WW individuals are white. in population of 1000 prairie mice, you find 500 black mice, 200 gray mice, and 300 white mice. calculate the genotypic frequencies. (Answer: BB=0.5, BW=0.2, WW=0.3). I know how to do this part.

2b) Let p be the frequency of B allele, and q be the frequency of the W allele. calculate p and q for this populatoin, and show your calculations. (Answer: p=0.6, q=0.4) The solution for p:( 2*500)+200/(2*1000).

Note: I thought I will have to use this equation, p=p2+1/2(2pq) to find allele frequency.

Solution

2 a). In the above question, we have to consider the total number of mice in the population i.e 500 + 200+ 300=1000

So,genotype frequency will be as follows:

BB(p²) = 500 / 1000 =0.5 ans

BW(2pq) = 200 / 1000 = 0.2 ans

WW(q²) = 300 / 1000 = 0.3 ans

2 b) Allelic frequencies will be as follows:

Frequency of B i.e p = p² + 1/2 (2pq)

= 0.5 + 0.2/2

=0.5 + 0.1

=0.6 ( ans )

Frequency of W i.e q = q² + 1/2 (2pq)

= 0.3 + 0.2/2

=0.3 + 0.1

=0.4 (ans)