Find out the number of heterozygous free ear lobed persons in a population of 3000 if the proportion of fused ear lobed persons is 9%:

Options

A. 1260
B. 1470
C. 270
D. 2730

Answer

To solve the problem of finding the number of heterozygous free ear lobed persons in a population of 3000, given that 9% of the population has fused ear lobes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Population**:
The total population is given as 3000 individuals.

2. **Calculate the Number of Fused Ear Lobed Individuals**:
Since 9% of the population has fused ear lobes, we can calculate the number of individuals with fused ear lobes:
\[ \text{Number of Fused Ear Lobed Individuals} = \frac{9}{100} \times 3000 = 270 \]

3. **Determine the Genotype Frequencies**:
In genetics, the trait for ear lobes can be represented as follows:
- Let \( p \) be the frequency of the dominant allele (free ear lobes).
- Let \( q \) be the frequency of the recessive allele (fused ear lobes).
- According to the Hardy-Weinberg principle, \( p + q = 1 \).

Since fused ear lobes are recessive, the individuals with fused ear lobes (genotype \( qq \)) can be represented as:
\[ q^2 = \frac{\text{Number of Fused Ear Lobed Individuals}}{\text{Total Population}} = \frac{270}{3000} = 0.09 \]

4. **Calculate the Frequency of the Recessive Allele (\( q \))**:
To find \( q \), we take the square root of \( q^2 \):
\[ q = \sqrt{0.09} = 0.3 \]

5. **Calculate the Frequency of the Dominant Allele (\( p \))**:
Using the relationship \( p + q = 1 \):
\[ p = 1 - q = 1 - 0.3 = 0.7 \]

6. **Calculate the Frequency of Heterozygous Individuals**:
The frequency of heterozygous individuals (genotype \( pq \)) can be calculated as:
\[ 2pq = 2 \times p \times q = 2 \times 0.7 \times 0.3 = 0.42 \]

7. **Calculate the Number of Heterozygous Free Ear Lobed Individuals**:
Finally, to find the number of heterozygous free ear lobed individuals in the population:
\[ \text{Number of Heterozygous Free Ear Lobed Individuals} = 2pq \times \text{Total Population} = 0.42 \times 3000 = 1260 \]

### Final Answer:
The number of heterozygous free ear lobed persons in a population of 3000 is **1260**.

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