In a population of 100 cats , 36 were white and 64 were black . If the black allele is dominant over white allele , what is the frequency of black allele in this population of cats ?

Options

A. 0.64
B. 0.4
C. 0.6
D. 0.48

Answer

To solve the problem of finding the frequency of the black allele in a population of cats, we can follow these steps:

### Step 1: Identify the total population and the number of each phenotype
In the given population of 100 cats:
- Number of white cats = 36
- Number of black cats = 64

### Step 2: Determine the genotype of the phenotypes
Since the black allele is dominant over the white allele, the white cats must be homozygous recessive (genotype = qq). Therefore, all white cats represent the recessive phenotype.

### Step 3: Calculate the frequency of the recessive phenotype
The frequency of the recessive phenotype (white cats) can be calculated as:
\[ \text{Frequency of white cats (q²)} = \frac{\text{Number of white cats}}{\text{Total population}} = \frac{36}{100} = 0.36 \]

### Step 4: Calculate the frequency of the recessive allele (q)
To find the frequency of the recessive allele (q), we take the square root of the frequency of the recessive phenotype:
\[ q = \sqrt{q²} = \sqrt{0.36} = 0.6 \]

### Step 5: Calculate the frequency of the dominant allele (p)
Using the Hardy-Weinberg principle, we know that:
\[ p + q = 1 \]
Substituting the value of q:
\[ p + 0.6 = 1 \]
Thus, solving for p gives:
\[ p = 1 - 0.6 = 0.4 \]

### Step 6: Conclusion
The frequency of the black allele (p) in this population of cats is:
\[ \text{Frequency of black allele} = p = 0.4 \]

### Final Answer
The frequency of the black allele in this population of cats is **0.4** (Option B).

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