Some people are hypersensitive to the smell of asparagus, and can even detect a

Question

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 As genotypes) can smell asparagus in urine, whereas a person with two copies of the alternative "a" allele (aa genotypes) cannot. Assume that men and women in the population have the same allele for 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.

Explanation / Answer

answer of part(a)

p(A)=0.05

p(a)=0.95

gametic population structure 0.05A+0.95a

genotypic population structure (0.05A+0.95a)2=0.05*0.05AA+2*0.05*0.95Aa+0.95*0.95aa

probability that a randomly sampled individual from the population has two copies of the a allele=

p(aa)=0.95*0.95=0.9025

answer of part(b)

Aa x Aa  will produce 25% aa

so required probability will be =(1/4)*2*0.05*0.95=0.002256

answer of part(c)

p(Aa)=0.095

required probability=0.095x0.095=0.009025

answer of part (d)

Aa x Aa will give 50% of Aa

so required probability will be 1/2*(.009025)=0.0045125

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