# Calculating the frequency of a recessive allele in case of three segregating alleles

Is it correct to say:

A. f(A) = p; f(a) = q
B. p = f(AA) + ½ f(Aa)=$\sqrt{f(AA)}$?

Also,

For a gene locus segregating more than two alleles, the frequency of each allele is the frequency of its homozygote plus 1/2 the sum of the frequencies of all heterozygotes in which it can occur.

For example, I have this data on blood-types from a population: 42,4% type A, 8.3% type B, 1.4% type AB, 47.9% type O. Plus we know that p(A)=0.250, p(B)=0,050, p(O)=0,692.
When I try to calculate p(O) in different ways, I get p(O)= $\sqrt{0.479}$=0,692
If I calculate p(O) as:p(O)= 0.479+½*0.424+½*0,083=0,7325
As the result, I am getting two different frequencies for p(O). What am I getting wrong here?

Welcome to Biology.SE

You should always limit your post to a single question.

Make sure to define what the function f() and p() mean.

Use points (.) instead of comas (,) for the numbers.

You should show how you made your calculations otherwise we can't tell what is right and wrong.

is $p = f(AA) + \frac1{1}{2} f(Aa)=\sqrt{f(AA)}$ correct?
$$f(AA) = p^2$$ $$f(Aa) = 2pq = 2p(1-p)$$ $$f(Aa)/2 = pq = p(1-p) = p - p^2$$ , therefore
$$f(AA) + f(Aa)/2 = p^2 + (p - p^2) = p = \sqrt{p^2} = \sqrt{f(AA)}$$