After graduation, you and 19 friends build a raft, sail to a deserted island, and start a new population, totally isolated from the world. Two of your friends carry (that is, are heterozygous for) the recessive cf allele, which in homozygotes causes cystic fibrosis. Assuming that the frequency of this allele does not change (your population is at HWE) as the population grows, what will be the instance of cystic fibrosis on your island once the population grows large?

Incidence of cystic fibrosis on the island = 0.0025

Explanation:

According to the given information, the population is in Hardy Weinberg equilibrium which means that the allele frequencies would be maintained over generations.

Given that total population size is = 20

Total number of alleles = 20 x 2 = 40 (since human are diploid, each individual has two alleles for one gene).

Out of total 19 people, only two are heterozygous for cystic fibrosis which means that out of total 40 alleles, the number of recessive allele for cystic fibrosis is = 2

Frequency of recessive allele (q) = 2 / 40 = 0.05

Frequency of cystic fibrosis genotype (q^2) = 0.05 x 0.05 = 0.0025

Therefore, incidence of cystic fibrosis on the island would be = 0.0025