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
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:
- be the frequency of the dominant allele.
- be the frequency of the recessive allele.
The equation representing the relationship between the allele frequencies is:
The equation representing the genotype frequencies is:
Here, cystic fibrosis is a recessive condition, which means individuals affected by it must have the homozygous recessive genotype (). The problem states that 1 in 2500 babies is affected. Therefore, the frequency of the homozygous recessive genotype () is:
To find the frequency of the recessive allele (), we take the square root of :
Now, we can find the frequency of the dominant allele () using the relation :
Thus, the frequency of the dominant allele in this population is 0.98.
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