Question

If the frequency of aa genotype is 0.04, the frequency of AA genotype will be which of the following?

• A. 0.40
• B. 0.60
• C. 0.80
• D. 0.64

Hint:

Always find the recessive allele frequency (\(q\)) first by taking the square root of the recessive genotype frequency (\(q^2\)). This avoids multi-variable confusion.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Under Hardy-Weinberg equilibrium, allele and genotype frequencies are mathematically related through the allele frequency equation:
\[ p + q = 1 \]
where \(p\) is the frequency of the dominant allele (A) and \(q\) is the frequency of the recessive allele (a).

Step 2: Key Formula or Approach:
The genotype frequencies are represented as:
\[ f(\text{AA}) = p^2 \]
\[ f(\text{Aa}) = 2pq \]
\[ f(\text{aa}) = q^2 \]

Step 3: Detailed Explanation:
Given:
\[ f(\text{aa}) = q^2 = 0.04 \]
Taking the square root on both sides:
\[ q = \sqrt{0.04} = 0.2 \]
Using the allele frequency relation:
\[ p = 1 - q = 1 - 0.2 = 0.8 \]
Now, calculate the frequency of the AA genotype:
\[ f(\text{AA}) = p^2 = (0.8)^2 = 0.64 \]

Step 4: Final Answer
The frequency of the AA genotype is 0.64.