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In chickens, a flat single comb is a recessive trait, while the short, thick rose comb is dominant. In a particular population of chickens, 45 are homozygous for the dominant trait, 30 are heterozygous dominant, and 25 have the recessive trait. Which expression is the correct way to calculate the frequency of the recessive allele?

A. [tex]$\frac{80}{100}$[/tex]
B. [tex]$\frac{80}{200}$[/tex]
C. [tex]$\frac{65}{100}$[/tex]
D. [tex]$\frac{65}{200}$[/tex]
E. [tex]$\frac{120}{200}$[/tex]



Answer :

GinnyAnswer
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]

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