In a large, randomly mating population, only one person in 10,000 is an albino. What will be the frequency of a carrier person of albinism?

Options

A. 1 in 50
B. 99 in 10000
C. 2 in 10000
D. 1 in 100

Explanation

To solve the problem of determining the frequency of carrier individuals for albinism in a large, randomly mating population where only one person in 10,000 is albino, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Genetic Basis of Albinism**:
- Albinism is an autosomal recessive genetic disorder. This means that an individual must inherit two copies of the recessive allele (let's denote it as 'a') to express the phenotype (albino). Individuals with one dominant allele (A) and one recessive allele (a) are carriers but do not express the phenotype.

2. **Determine the Frequency of the Recessive Phenotype**:
- Given that 1 in 10,000 individuals is albino, we can express this frequency as:
\[ q^2 = \frac{1}{10,000} = 0.0001 \]

3. **Calculate the Frequency of the Recessive Allele (q)**:
- To find the frequency of the recessive allele (q), we take the square root of the frequency of the recessive phenotype:
\[ q = \sqrt{q^2} = \sqrt{0.0001} = 0.01 \]

4. **Calculate the Frequency of the Dominant Allele (p)**:
- Using the Hardy-Weinberg principle, we know that:
\[ p + q = 1 \]
- Substituting the value of q:
\[ p = 1 - q = 1 - 0.01 = 0.99 \]

5. **Calculate the Frequency of Carrier Individuals (2pq)**:
- The frequency of heterozygous individuals (carriers) is given by the formula:
\[ 2pq \]
- Substituting the values of p and q:
\[ 2pq = 2 \times 0.99 \times 0.01 = 0.0198 \]

6. **Convert the Frequency of Carriers to a Ratio**:
- To express this frequency in terms of a ratio, we can convert 0.0198 to a fraction:
\[ 0.0198 \approx 0.02 \quad \text{(or 2%)} \]
- In terms of individuals, this means that approximately 2 out of every 100 individuals are carriers, which can also be expressed as:
\[ \frac{1}{50} \quad \text{(since 2 out of 100 simplifies to 1 out of 50)} \]

### Final Answer:
The frequency of carrier individuals for albinism in this population is **1 in 50**.

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