Refer to Assignment Problem 36. If a randomly sampled child has the aa genotype, what is the probability that both its parents were also aa?

Data from problem 36

Some people are hypersensitive to the smell of asparagus, and can even detect a strong odor in the urine of a person who has recently eaten asparagus. This trait turns out to have a simple genetic basis. An individual with one or two copies of the A allele at the gene (AA or Aa genotypes) can smell asparagus in urine, whereas a person with two copies of the alternative “a” allele (aa genotypes) cannot (Online Mendelian Inheritance in Man 2019). Assume that men and women in the population have the same allele frequencies at the asparagus-smelling gene and that marriage and child production are independent of the genotype at the gene. In the human population, 5% of alleles are A and 95% are a.

a. What is the probability that a randomly sampled individual from the population has two copies of the a allele (that is, that it has an aa genotype)?

b. What is the probability that both members of a randomly sampled married couple (man and woman) are aa at the asparagus-smelling gene?

c. What is the probability that both members of a randomly sampled married couple (man and woman) are heterozygotes at this locus (meaning that each person has one allele A and one allele a)?

d. Consider the type of couple described in (c). What is the probability that the first child of such a couple also has one A allele and one a allele (is a heterozygote)? Remember that the child must receive exactly one allele from each parent.