Cystic fibrosis is an autosomal recessive condition. In a population, 0.04% of individuals have the disease. Use the Hardy-Weinberg equation to calculate the number of carriers of cystic fibrosis.

Autosomal recessive means that 2 copies of a allele are required for the phenotype. The phenotype is the set of observable characteristics due to the genotype. In this case the phenotype is whether an individual has cystic fibrosis.

The Harvey-Weinberg equation is:

p + q = 1

(p+q)² = 1

p² + 2pq + q² = 1

Where p is the dominant allele, and q is the recessive allele, that causes the disease when found with another q.

Therefore p² represents the proportion of unaffected individuals, 2pq represents the proportion of carriers and q² represents the proportion of individuals with the disease.

q² is therefore equal to 1/2500 (0.04%). q is therefore equal to 1/50. p is therefore equal to 49/50. The proportion of carriers is therefore equal to 1/50 x 49/50 x 2 = 0.0392