p = frequency of the dominant allele (A, normal pigmentation)

Question

ScanSolve AI Tutor · Accepted Answer

To solve this problem, we will use the Hardy-Weinberg principle, which describes the genetic equilibrium in a randomly mating population.

Let:
$p$ = frequency of the dominant allele (A, normal pigmentation)
$q$ = frequency of the recessive allele (a, albinism)

The Hardy-Weinberg equations are:

Allele frequencies: $p + q = 1$
Genotype frequencies: $p^2 + 2pq + q^2 = 1$ $p^{2} + 2 pq + q^{2} = 1$
- $p^2$ represents the frequency of homozygous dominant individuals (AA).
- $2pq$ represents the frequency of heterozygous individuals (Aa, carriers).
- $q^2$ represents the frequency of homozygous recessive individuals (aa, individuals with albinism).

Given information:
Total population (N) = 10,000 individuals
Number of individuals with albinism (recessive trait, aa) = 1,600

Calculate the frequency of the homozygous recessive genotype ( $q^2$ ).
The frequency of individuals with albinism is the number of affected individuals divided by the total population.
$q^2 = \frac{\text{Number of individuals with albinism}}{\text{Total population}}$ $q^2 = \frac{1600}{10000}$ $q^2 = 0.16$
Calculate the frequency of the recessive allele ( $q$ ).
Take the square root of $q^2$ .
$q = \sqrt{0.16}$ $q = 0.4$
Calculate the frequency of the dominant allele ( $p$ ).
Using the allele frequency equation $p + q = 1$ :
$p = 1 - q$ $p = 1 - 0.4$ $p = 0.6$
Calculate the frequency of carriers ($2pq$).
Carriers are heterozygous individuals (Aa).
$2pq = 2 \times p \times q$ $2pq = 2 \times 0.6 \times 0.4$ $2pq = 2 \times 0.24$ $2pq = 0.48$
Calculate the number of carriers in the population.
Multiply the frequency of carriers by the total population.
$\text{Number of carriers} = 2pq \times \text{Total population}$ $\text{Number of carriers} = 0.48 \times 10000$ $\text{Number of carriers} = 4800$
The number of individuals in this population who are "CARRIERS" of the albino allele is 4,800.

Comparing this to the given options:
A) 8,400
B) 4,800
C) 3,600
D) 480

The correct option is B.

The final answer is $\boxed{\text{B) 4,800}}$ .

Answer