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 question of finding the number of heterozygous free earlobed persons in a population of 3000, given that the proportion of fused earlobed persons is 9%, we can follow these steps:

### Step-by-Step Solution:

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

2. **Calculate the Number of Fused Earlobed Persons**:
The proportion of fused earlobed persons is 9%. To find the number of fused earlobed persons, we calculate:
\[ \text{Number of fused earlobed persons} = 9\% \text{ of } 3000 = \frac{9}{100} \times 3000 = 270 \]

3. **Calculate the Number of Free Earlobed Persons**:
To find the number of free earlobed persons, we subtract the number of fused earlobed persons from the total population:
\[ \text{Number of free earlobed persons} = 3000 - 270 = 2730 \]

4. **Use the Hardy-Weinberg Principle**:
According to the Hardy-Weinberg principle, we can denote the frequency of the dominant allele (free earlobes) as \( p \) and the frequency of the recessive allele (fused earlobes) as \( q \). Since fused earlobes are recessive, the proportion of fused earlobed individuals (homozygous recessive) is given by \( q^2 \):
\[ q^2 = \frac{270}{3000} = 0.09 \]
To find \( q \), we take the square root:
\[ q = \sqrt{0.09} = 0.3 \]

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

6. **Calculate the Number of Heterozygous Free Earlobed Persons**:
The frequency of heterozygous individuals (carriers of the free earlobe trait) is given by \( 2pq \):
\[ 2pq = 2 \times 0.7 \times 0.3 = 0.42 \]
To find the number of heterozygous individuals in the population:
\[ \text{Number of heterozygous free earlobed persons} = 0.42 \times 3000 = 1260 \]

### Final Answer:
The number of heterozygous free earlobed persons in the population of 3000 is **1260**.

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