Three variants of the gene encoding the -globin component of hemoglobin occur in the human population of

Three variants of the gene encoding the β-globin component of hemoglobin occur in the human population of the Kassena-Nankana district of Ghana, West Africa. The most frequent allele, A, occurs at frequency 0.83.

The two other variants, S (“sickle cell”) and C, occur at frequency 0.04 and 0.13, respectively (Ghansah et al. 2012). Each individual has two alleles, determining its genotype at the β-globin gene. Assume that knowing the identity of one of the alleles of any individual provides no information about the identity of the second allele (i.e., alleles occur independently in individuals).

 a. CC individuals, having two copies of allele C, are slightly anemic. What is the probability that a randomly sampled individual from the population has two copies of the C allele (in other words, what is the probability that the individual’s first allele is C and his or her second allele is also C)?

b. What is the probability that a randomly sampled individual is a homozygote (has two copies of the same allele)?

c. Compared with AA individuals, AS and AC individuals are largely resistant to malaria, which is endemic to the region. They also experience fewer deleterious side effects than SS and CC individuals. What is the probability that a randomly sampled individual is AS? (Remember that an individual can be AS by getting A from mom and S from dad or by getting S from mom and A from dad.)

d. What is the probability that a randomly sampled individual is AS or AC?