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 of finding the frequency of heterozygotes in a population with an autosomal recessive gene frequency of 0.4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the frequency of the recessive allele (q)**:
- Given that the frequency of the recessive gene (q) is 0.4.

2. **Calculate the frequency of the dominant allele (p)**:
- According to the Hardy-Weinberg principle, p + q = 1.
- Therefore, p = 1 - q = 1 - 0.4 = 0.6.

3. **Use the Hardy-Weinberg equation to find the frequency of heterozygotes (2pq)**:
- The frequency of heterozygotes is given by the formula 2pq.
- Substitute the values of p and q into the equation:
- 2pq = 2 * (0.6) * (0.4) = 2 * 0.24 = 0.48.

4. **Calculate the number of heterozygotes in the population**:
- To find the actual number of heterozygotes in a population of 4000 individuals, multiply the frequency of heterozygotes by the total number of individuals:
- Number of heterozygotes = 0.48 * 4000 = 1920.

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

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