Let's break down the process step by step to find the frequency of the recessive allele in the given population of chickens.
First, let's identify the given numbers:
- The number of chickens that are homozygous dominant (RR) = 45
- The number of chickens that are heterozygous dominant (Rr) = 30
- The number of chickens that are homozygous recessive (rr) = 25
Next, calculate the total number of chickens:
[tex]\[ \text{Total chickens} = 45 + 30 + 25 = 100 \][/tex]
We need to find the total number of recessive alleles in the population. Each homozygous recessive (rr) chicken has 2 recessive alleles, and each heterozygous dominant (Rr) chicken has 1 recessive allele. Therefore:
[tex]\[ \text{Total recessive alleles} = (25 \times 2) + 30 = 50 + 30 = 80 \][/tex]
Now, calculate the total number of alleles in the population. Each chicken has 2 alleles, so:
[tex]\[ \text{Total alleles} = 100 \times 2 = 200 \][/tex]
The frequency of the recessive allele is then the number of recessive alleles divided by the total number of alleles:
[tex]\[ \text{Frequency of recessive allele} = \frac{\text{Total recessive alleles}}{\text{Total alleles}} = \frac{80}{200} \][/tex]
So the correct expression for the frequency of the recessive allele is:
[tex]\[ \boxed{\frac{80}{200}} \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
