To answer this question, let's analyze the data and the necessary steps to calculate the frequency of the recessive allele in the population of chickens. Here is a step-by-step solution:
1. Total number of chickens:
- There are 45 chickens that are homozygous dominant (AA).
- There are 30 chickens that are heterozygous dominant (Aa).
- There are 25 chickens that have the recessive trait (aa).
- Therefore, the total number of chickens is:
[tex]\[
45 + 30 + 25 = 100
\][/tex]
2. Calculate the total number of alleles:
- Since each chicken has two alleles for the comb trait, the total number of alleles in all the chickens is:
[tex]\[
100 \times 2 = 200
\][/tex]
3. Calculate the number of recessive alleles (a):
- Homozygous recessive (aa) chickens contribute 2 recessive alleles each. There are 25 homozygous recessive chickens:
[tex]\[
25 \times 2 = 50 \text{ recessive alleles}
\][/tex]
- Heterozygous dominant (Aa) chickens contribute 1 recessive allele each. There are 30 heterozygous dominant chickens:
[tex]\[
30 \times 1 = 30 \text{ recessive alleles}
\][/tex]
- Therefore, the total number of recessive alleles is:
[tex]\[
50 + 30 = 80
\][/tex]
4. Calculate the frequency of the recessive allele (a):
- The frequency of an allele is the number of copies of the allele divided by the total number of alleles in the population. Thus, the frequency of the recessive allele is:
[tex]\[
\text{Frequency of } a = \frac{\text{Number of } a \text{ alleles}}{\text{Total number of alleles}} = \frac{80}{200}
\][/tex]
Among the provided choices, the correct expression to calculate the frequency of the recessive allele is:
[tex]\[
\frac{80}{200}
\][/tex]
Thus, the correct answer is:
B. [tex]\(\frac{80}{200}\)[/tex].
