To determine the frequency of the recessive allele in a population of chickens, we can use the Hardy-Weinberg principle. Here's a step-by-step process:
1. Determine the number of each genotype:
- Homozygous dominant ([tex]\( RR \)[/tex]): 45 chickens
- Heterozygous dominant ([tex]\( Rr \)[/tex]): 30 chickens
- Homozygous recessive ([tex]\( rr \)[/tex]): 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 alleles:
Each chicken has 2 alleles. Therefore, the total number of alleles in the population is:
[tex]\[
\text{Total number of alleles} = 2 \times 100 = 200
\][/tex]
4. Calculate the total number of recessive alleles:
- Homozygous recessive (rr): Each homozygous recessive chicken contributes 2 recessive alleles. So, the total number of recessive alleles from [tex]\( rr \)[/tex] chickens is:
[tex]\[
25 \times 2 = 50
\][/tex]
- Heterozygous dominant (Rr): Each heterozygous chicken contributes 1 recessive allele. So, the total number of recessive alleles from [tex]\( Rr \)[/tex] chickens is:
[tex]\[
30 \times 1 = 30
\][/tex]
- Homozygous dominant (RR) do not contribute any recessive alleles.
Adding these together, the total number of recessive alleles is:
[tex]\[
50 + 30 = 80
\][/tex]
5. Calculate the frequency of the recessive allele:
The frequency of the recessive allele ( [tex]\( r \)[/tex] ) is the number of recessive alleles divided by the total number of alleles:
[tex]\[
\text{Frequency of } r = \frac{\text{Total number of recessive alleles}}{\text{Total number of alleles}} = \frac{80}{200}
\][/tex]
Simplifying this fraction:
[tex]\[
\frac{80}{200} = \frac{40}{100} = 0.4
\][/tex]
From the given options, the expression that correctly calculates the frequency of the recessive allele is:
[tex]\[
D. \frac{55}{200}
\][/tex]
However, upon careful consideration, the correct fraction representing the frequency is actually [tex]\( \frac{80}{200} \)[/tex]. But since the problem and the exact answers are given, we assume there might have been a misunderstanding. The actual result would guide you to choose the closest one if there are any discrepancies. Therefore, the direct correct answer is E: [tex]\( \frac{120}{200} = 0.6 \)[/tex] ratios would typically be insighted errors here.
