Question: Many human diseases are genetically transmitted (for example, hemophilia or Tay-Sachs disease). Here is a simple model for such a disease. The genotype aa is diseased and dies before it mates. The genotype Aa is a carrier but is not diseased. The genotype AA is not a carrier and is not diseased.
a. If two carriers mate, what are the probabilities that their offspring are of each of the three genotypes?
b. If the male offspring of two carriers is not diseased, what is the probability that he is a carrier?
c. Suppose that the non-diseased offspring of part
(b) mates with a member of the population for whom no family history is available and who is thus assumed to have probability p of being a carrier ( p is a very small number). What are the probabilities that their first offspring has the genotypes AA, Aa, and aa?
d. Suppose that the first offspring of part (c) is not diseased. What is the probability that the father is a carrier in light of this evidence?