Question Details

In the Caucasian population of the US, 1 in 2500 babies is affected by a recessive condition – cystic fibrosis. In this population, the frequency of the dominant allele is

Options

A

0.02

B

0.36

C

0.56

D

0.98

Correct Answer :

0.98

Solution :

The correct option is 0.98.

To find the frequency of the dominant allele in the population, we can apply the Hardy-Weinberg principle. According to this principle, the frequency of alleles and genotypes in a population remains constant from generation to generation in the absence of evolutionary influences.

Let:
- p be the frequency of the dominant allele.
- q be the frequency of the recessive allele.

The equation representing the relationship between the allele frequencies is:
p+q=1

The equation representing the genotype frequencies is:
p2+2pq+q2=1

Here, cystic fibrosis is a recessive condition, which means individuals affected by it must have the homozygous recessive genotype (q2). The problem states that 1 in 2500 babies is affected. Therefore, the frequency of the homozygous recessive genotype (q2) is:
q2=12500=0.0004

To find the frequency of the recessive allele (q), we take the square root of q2:
q=0.0004=0.02

Now, we can find the frequency of the dominant allele (p) using the relation p+q=1:
p=1-q
p=1-0.02=0.98

Thus, the frequency of the dominant allele in this population is 0.98.

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