A population is in Hardy-Weinberg equilibrium for a gene with only 2 alleles . If the gene frequency of an allele A is 0.7 , the genotypic frequency of homozygous recessive individuals will be

Options

A. `0.49`
B. `0.42`
C. `0.09`
D. `0.9`

Answer

To solve the problem, we will use the Hardy-Weinberg principle, which provides a way to calculate the frequencies of genotypes in a population that is in equilibrium. Here are the steps to find the genotypic frequency of homozygous recessive individuals:

### Step-by-Step Solution:

1. **Identify the Allele Frequencies**:
- We are given that the frequency of allele A (dominant) is \( p = 0.7 \).
- Since there are only two alleles (A and a), the frequency of allele a (recessive) can be calculated as:
\[ q = 1 - p = 1 - 0.7 = 0.3 \]

2. **Calculate the Genotypic Frequency of Homozygous Recessive Individuals**:
- The genotypic frequency of homozygous recessive individuals (aa) is given by \( q^2 \).
- We can calculate this as follows:
\[ q^2 = (0.3)^2 = 0.09 \]

3. **Conclusion**:
- Therefore, the genotypic frequency of homozygous recessive individuals (aa) in the population is \( 0.09 \).

### Answer:
The genotypic frequency of homozygous recessive individuals is **0.09** (Option C).