If the frequency of recesive phenotype is 9% then find out the number of homozygous organisms in population of 50,000 individuals:-

Options

A. 42000
B. 29000
C. 4500
D. 24500

Answer

To solve the problem of finding the number of homozygous organisms in a population of 50,000 individuals given that the frequency of the recessive phenotype is 9%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The frequency of the recessive phenotype (q²) is given as 9%. In decimal form, this is 0.09.

2. **Use the Hardy-Weinberg Principle**:
- According to the Hardy-Weinberg principle, the equation is:
\[ p^2 + 2pq + q^2 = 1 \]
- Here, \( q^2 \) represents the frequency of the homozygous recessive phenotype.

3. **Calculate q**:
- Since \( q^2 = 0.09 \), we can find \( q \) by taking the square root:
\[ q = \sqrt{0.09} = 0.3 \]

4. **Calculate p**:
- Using the relationship \( p + q = 1 \):
\[ p = 1 - q = 1 - 0.3 = 0.7 \]

5. **Calculate p²**:
- Now we can find \( p^2 \):
\[ p^2 = (0.7)^2 = 0.49 \]

6. **Determine the Number of Homozygous Individuals**:
- The number of homozygous dominant individuals (p²) in the population:
\[ \text{Homozygous Dominant} = p^2 \times \text{Total Population} = 0.49 \times 50,000 = 24,500 \]
- The number of homozygous recessive individuals (q²) in the population:
\[ \text{Homozygous Recessive} = q^2 \times \text{Total Population} = 0.09 \times 50,000 = 4,500 \]

7. **Total Number of Homozygous Individuals**:
- To find the total number of homozygous individuals (both homozygous dominant and homozygous recessive):
\[ \text{Total Homozygous} = \text{Homozygous Dominant} + \text{Homozygous Recessive} = 24,500 + 4,500 = 29,000 \]

### Final Answer:
The total number of homozygous organisms in the population of 50,000 individuals is **29,000**.

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