To determine the frequency of the recessive allele in the given population of chickens, follow these steps:
1. Identify the number of each genotype:
- Homozygous dominant (RR): \(45\) chickens
- Heterozygous dominant (Rr): \(30\) chickens
- Homozygous recessive (rr): \(25\) chickens
2. Calculate the total number of chickens:
[tex]\[
\text{Total number of chickens} = 45 + 30 + 25 = 100
\][/tex]
3. Calculate the total number of recessive alleles in the population:
- Each homozygous recessive chicken contributes \(2\) recessive alleles (rr), so:
[tex]\[
25 \times 2 = 50 \text{ recessive alleles}
\][/tex]
- Each heterozygous chicken contributes \(1\) recessive allele (Rr), so:
[tex]\[
30 \times 1 = 30 \text{ recessive alleles}
\][/tex]
[tex]\[
\text{Total recessive alleles} = 50 + 30 = 80
\][/tex]
4. Calculate the total number of alleles in the population:
Since each chicken has \(2\) alleles, the total number of alleles is:
[tex]\[
\text{Total alleles} = 100 \times 2 = 200
\][/tex]
5. Calculate the frequency of the recessive allele:
The frequency of the recessive allele is the ratio of the number of recessive alleles to the total number of alleles:
[tex]\[
\text{Frequency of recessive allele} = \frac{\text{Total recessive alleles}}{\text{Total alleles}} = \frac{80}{200}
\][/tex]
Thus, the correct expression to calculate the frequency of the recessive allele is:
[tex]\[
\boxed{\frac{80}{200}}
\][/tex]
