If the frequency of recessive phenotype in a stable population is `25%` , the frequency of the dominant allele in that population is

Options

A. `50%`
B. `40%`
C. `25%`
D. `10%`

Answer

To solve the problem of finding the frequency of the dominant allele in a stable population where the frequency of the recessive phenotype is 25%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The frequency of the recessive phenotype is given as 25%.
- In terms of Hardy-Weinberg equilibrium, this frequency corresponds to \( q^2 \), where \( q \) is the frequency of the recessive allele.

2. **Convert Percentage to Decimal**:
- Convert 25% to decimal form:
\[ q^2 = 0.25 \]

3. **Calculate the Frequency of the Recessive Allele (q)**:
- To find \( q \), take the square root of \( q^2 \):
\[ q = \sqrt{0.25} = 0.5 \]

4. **Use the Hardy-Weinberg Principle**:
- According to the Hardy-Weinberg principle, the sum of the frequencies of the dominant allele (p) and the recessive allele (q) must equal 1:
\[ p + q = 1 \]

5. **Calculate the Frequency of the Dominant Allele (p)**:
- Substitute the value of \( q \) into the equation:
\[ p + 0.5 = 1 \]
- Solve for \( p \):
\[ p = 1 - 0.5 = 0.5 \]

6. **Convert the Frequency of the Dominant Allele to Percentage**:
- Convert \( p \) back to percentage form:
\[ p = 0.5 \times 100 = 50\% \]

### Final Answer:
The frequency of the dominant allele in the population is **50%**.

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