7. In humans, ABO blood type is controlled by a single gene with2 codominant alleles (I^A and I^B) and onerecessive allele (i).  The population of humans in thecity of Xanadu is 7568.  1874 of these people have bloodtype O and 1243 of these people have homozygous blood typeA.  You will need to use a three-variable Hardy-Weinbergequation for this question: p² + 2pq + q² +2qr + r² + 2pr = 1.  Note that p + q + r =1.

a. (2 points) What are the frequenciesof the I^A, I^B, and i alleles assuming thispopulation is randomly mating and there are no significantevolutionary forces acting on the population?

b. (2 points) Estimate how manyindividuals in the population have each of the following genotypes:I^Ai, I^AI^B,I^BI^B, and I^Bi.

c. (2 points) Estimate how many individuals in the populationhave type A, type B, type AB, and type O blood.

d. (2 points) A disease suddenlyemerges that kills 60% of people with type A blood (leaving 40%alive), kills 40% of people with type AB blood, kills 10% of allpeople with type B blood, and kills 5% of all people with type Oblood. What is the frequency of each blood type in the populationnow?

e. (2 points) An effective vaccine isdeveloped so the disease only affects a single generation. Usingthe values for the number of survivors with type O and homozygoustype A blood, determine what the allele frequencies of theI^A, I^B and i alleles will be when thepopulation of Xanadu has again reached Hardy-Weinbergequilibrium.