The frequency of an autosomal recessive gene is 0.4. Then what will be the frequency of heterozygotes in progeny among 4000 individual ?

Options

A. 2000
B. 1920
C. 2400
D. 1600

Answer

To solve the problem, we need to determine the frequency of heterozygotes in a population where the frequency of an autosomal recessive gene is given as 0.4. We will use the Hardy-Weinberg principle to find the required values step by step.

### Step-by-Step Solution:

1. **Identify the given frequency of the recessive allele (q)**:
- The frequency of the autosomal recessive gene (q) is given as 0.4.

2. **Calculate the frequency of the dominant allele (p)**:
- According to the Hardy-Weinberg principle, the sum of the frequencies of the two alleles (p + q) is equal to 1.
- Therefore, we can calculate p as follows:
\[ p = 1 - q = 1 - 0.4 = 0.6 \]

3. **Calculate the frequency of heterozygotes (2pq)**:
- The frequency of heterozygotes (2pq) can be calculated using the formula:
\[ 2pq = 2 \times p \times q \]
- Substituting the values of p and q:
\[ 2pq = 2 \times 0.6 \times 0.4 = 0.48 \]

4. **Calculate the number of heterozygotes in a population of 4000 individuals**:
- To find the actual number of heterozygotes in the population, multiply the frequency of heterozygotes by the total number of individuals:
\[ \text{Number of heterozygotes} = 0.48 \times 4000 \]
- Performing the calculation:
\[ \text{Number of heterozygotes} = 1920 \]

### Final Answer:
The frequency of heterozygotes in progeny among 4000 individuals is **1920**.

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