Final answer:
The frequency of the wild-type (βA) allele in the population is approximately 0.72 (72%), the frequency of the mutant (βS) allele is approximately 0.28 (28%), and the frequency of carriers (heterozygotes) for sickle cell disease (SCD) is about 0.41 (41%).
Step-by-step explanation:
To find the frequency of the wild-type allele (βA) and the mutant allele (βS) in the population, we will use the Hardy-Weinberg equation:
p² + 2pq + q² = 1
p is the frequency of the dominant allele (βA)
q is the frequency of the recessive allele (βS)
pq represents the frequency of the heterozygous genotype.
Given that 8 in 100 newborn infants have SCD (q²), we find q by taking the square root of 0.08, which gives us q ≈ 0.2828.
Using p + q = 1, we can calculate p ≈ 1 - 0.2828 ≈ 0.7172.
Therefore, the frequency of the wild-type (βA) allele is approximately 0.72 (72%), and the frequency of the mutant (βS) allele is approximately 0.28 (28%).
To determine the frequency of carriers of SCD (heterozygotes, 2pq), we multiply 2 by the frequency of each allele,
2 × 0.7172 × 0.2828 ≈ 0.4065 or 40.65%.