To determine the frequency of the recessive allele in a population of chickens with given genotypes, let's follow the steps below:
1. Count the number of individuals with each genotype:
- Homozygous dominant (RR): 45 chickens
- Heterozygous dominant (Rr): 30 chickens
- Recessive trait (rr): 25 chickens
2. Calculate the total number of chickens:
[tex]\[
\text{Total chickens} = 45 + 30 + 25 = 100
\][/tex]
3. Determine the number of dominant alleles:
- Each homozygous dominant (RR) chicken contributes 2 dominant alleles:
[tex]\[
45 \times 2 = 90 \quad (\text{alleles})
\][/tex]
- Each heterozygous dominant (Rr) chicken contributes 1 dominant allele:
[tex]\[
30 \times 1 = 30 \quad (\text{alleles})
\][/tex]
[tex]\[
\text{Total dominant alleles} = 90 + 30 = 120
\][/tex]
4. Determine the total number of alleles in the population:
- Since each chicken has 2 alleles, the total number of alleles is:
[tex]\[
100 \times 2 = 200
\][/tex]
5. Calculate the number of recessive alleles:
- The number of recessive alleles is the total number of alleles minus the number of dominant alleles:
[tex]\[
\text{Recessive alleles} = 200 - 120 = 80
\][/tex]
6. Calculate the frequency of the recessive allele:
- The frequency is the number of recessive alleles divided by the total number of alleles:
[tex]\[
\text{Frequency of recessive allele} = \frac{80}{200} = 0.4
\][/tex]
Given the steps above, the correct expression for calculating the frequency of the recessive allele is:
B. [tex]\(\frac{80}{200}\)[/tex]
