Answer :
To solve this problem about the frequency of the recessive allele within the given population of chickens, here’s a step-by-step solution:
1. Identify the Genotype Counts:
- Homozygous Dominant (RR): 45 chickens
- Heterozygous Dominant (Rr): 30 chickens
- Recessive Trait (rr): 25 chickens
2. Calculate the Total Number of Chickens:
Adding together all the chickens:
[tex]\[ \text{Total Chickens} = 45 (\text{Homozygous Dominant}) + 30 (\text{Heterozygous Dominant}) + 25 (\text{Recessive Trait}) = 100 \][/tex]
3. Calculate the Total Number of Alleles:
Each chicken has two alleles, so:
[tex]\[ \text{Total Alleles} = 2 \times \text{Total Chickens} = 2 \times 100 = 200 \][/tex]
4. Calculate the Number of Recessive Alleles:
- Homozygous Dominant (RR) contributes 0 recessive alleles.
- Heterozygous (Rr) contributes 1 recessive allele per chicken.
- Homozygous Recessive (rr) contributes 2 recessive alleles per chicken.
Therefore:
[tex]\[ \text{Recessive Alleles} = 0 \times 45 + 1 \times 30 + 2 \times 25 = 0 + 30 + 50 = 80 \][/tex]
5. Calculate the Frequency of the Recessive Allele (q):
The frequency of an allele is the number of that type of allele divided by the total number of alleles.
[tex]\[ \text{Frequency of Recessive Allele} = \frac{\text{Number of Recessive Alleles}}{\text{Total Number of Alleles}} = \frac{80}{200} \][/tex]
6. Match the Frequency to the Given Choices:
Let’s look at the provided options:
- A. [tex]\(\frac{80}{100}\)[/tex]
- B. [tex]\(\frac{80}{200}\)[/tex]
- C. [tex]\(\frac{55}{100}\)[/tex]
- D. [tex]\(\frac{55}{200}\)[/tex]
- E. [tex]\(\frac{120}{200}\)[/tex]
The correct frequency of the recessive allele, as calculated, matches option B: [tex]\(\frac{80}{200}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
1. Identify the Genotype Counts:
- Homozygous Dominant (RR): 45 chickens
- Heterozygous Dominant (Rr): 30 chickens
- Recessive Trait (rr): 25 chickens
2. Calculate the Total Number of Chickens:
Adding together all the chickens:
[tex]\[ \text{Total Chickens} = 45 (\text{Homozygous Dominant}) + 30 (\text{Heterozygous Dominant}) + 25 (\text{Recessive Trait}) = 100 \][/tex]
3. Calculate the Total Number of Alleles:
Each chicken has two alleles, so:
[tex]\[ \text{Total Alleles} = 2 \times \text{Total Chickens} = 2 \times 100 = 200 \][/tex]
4. Calculate the Number of Recessive Alleles:
- Homozygous Dominant (RR) contributes 0 recessive alleles.
- Heterozygous (Rr) contributes 1 recessive allele per chicken.
- Homozygous Recessive (rr) contributes 2 recessive alleles per chicken.
Therefore:
[tex]\[ \text{Recessive Alleles} = 0 \times 45 + 1 \times 30 + 2 \times 25 = 0 + 30 + 50 = 80 \][/tex]
5. Calculate the Frequency of the Recessive Allele (q):
The frequency of an allele is the number of that type of allele divided by the total number of alleles.
[tex]\[ \text{Frequency of Recessive Allele} = \frac{\text{Number of Recessive Alleles}}{\text{Total Number of Alleles}} = \frac{80}{200} \][/tex]
6. Match the Frequency to the Given Choices:
Let’s look at the provided options:
- A. [tex]\(\frac{80}{100}\)[/tex]
- B. [tex]\(\frac{80}{200}\)[/tex]
- C. [tex]\(\frac{55}{100}\)[/tex]
- D. [tex]\(\frac{55}{200}\)[/tex]
- E. [tex]\(\frac{120}{200}\)[/tex]
The correct frequency of the recessive allele, as calculated, matches option B: [tex]\(\frac{80}{200}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
