If the frequency of a recessive allele is 0.4. What will be the frequency of individuals with dominant phenotype in the population?

Options

A. 0.68
B. 0.6
C. 0.84
D. 0.36

Answer

To solve the problem, we will use the Hardy-Weinberg principle, which provides a mathematical model for studying genetic variation in a population. Here's a step-by-step solution:

### Step 1: Understand the given information
We are given that the frequency of a recessive allele (denoted as 'q') is 0.4. This means:
- \( q = 0.4 \)

### Step 2: Calculate the frequency of the dominant allele
According to the Hardy-Weinberg principle, the sum of the frequencies of the dominant allele (denoted as 'p') and the recessive allele (denoted as 'q') must equal 1:
- \( p + q = 1 \)

Substituting the value of \( q \):
- \( p + 0.4 = 1 \)
- \( p = 1 - 0.4 = 0.6 \)

### Step 3: Calculate the frequency of individuals with the dominant phenotype
The frequency of individuals with the dominant phenotype includes both homozygous dominant (represented as \( p^2 \)) and heterozygous (represented as \( 2pq \)) individuals. Therefore, we need to calculate:
- \( p^2 + 2pq \)

#### Step 3a: Calculate \( p^2 \)
- \( p^2 = (0.6)^2 = 0.36 \)

#### Step 3b: Calculate \( 2pq \)
- \( 2pq = 2 \times (0.6) \times (0.4) = 2 \times 0.24 = 0.48 \)

### Step 4: Add the frequencies to find the total frequency of the dominant phenotype
Now we can add the frequencies of the homozygous dominant and heterozygous individuals:
- Total frequency of dominant phenotype = \( p^2 + 2pq = 0.36 + 0.48 = 0.84 \)

### Final Answer
The frequency of individuals with the dominant phenotype in the population is **0.84**.

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