What is the number of tongue roller persons in a population of 4000 if frequency of non-roller allele is 0.4 ?

Options

A. 3360
B. 1920
C. 1440
D. 640

Answer

To solve the problem of finding the number of tongue roller persons in a population of 4000, given that the frequency of the non-roller allele is 0.4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Allele Frequencies**:
- Let \( q \) be the frequency of the non-roller allele. Given \( q = 0.4 \).
- To find the frequency of the roller allele \( p \), we use the equation \( p + q = 1 \).
- Therefore, \( p = 1 - q = 1 - 0.4 = 0.6 \).

2. **Apply Hardy-Weinberg Principle**:
- The Hardy-Weinberg principle states that the genotype frequencies can be calculated using the formula:
\[ p^2 + 2pq + q^2 = 1 \]
- Here, \( p^2 \) represents the frequency of homozygous dominant individuals (rollers), \( 2pq \) represents the frequency of heterozygous individuals (rollers), and \( q^2 \) represents the frequency of homozygous recessive individuals (non-rollers).

3. **Calculate Genotype Frequencies**:
- Calculate \( p^2 \):
\[ p^2 = (0.6)^2 = 0.36 \]
- Calculate \( 2pq \):
\[ 2pq = 2 \times 0.6 \times 0.4 = 0.48 \]
- The total frequency of tongue rollers (both homozygous dominant and heterozygous) is:
\[ \text{Frequency of rollers} = p^2 + 2pq = 0.36 + 0.48 = 0.84 \]

4. **Calculate the Number of Tongue Rollers**:
- To find the number of tongue rollers in a population of 4000, multiply the frequency of rollers by the total population:
\[ \text{Number of tongue rollers} = 0.84 \times 4000 = 3360 \]

5. **Final Answer**:
- The number of tongue roller persons in the population of 4000 is **3360**.