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 indivigual with one or two copies of the A allele at the gene can smell asparagus in urine, whereas a person with two copies of the alternative "a" allele (aa genotypes) cannot. Assume that men and woman in the popultation hae the same allele frequencies at the asparagus-smelling gene and that marriage and children production are independent of the genotype at the gene. In the human population, 5% of alleles are A and 95% are a. If a randomly selected child has the aa genotype, what is the probability that both its parents were also aa?

Explanation / Answer

As each child is independent we have sample space

as aa, aA, AA, Aa with equal probabilities = 1/4

Hence for a random child to have aa genotype

Probability =1/4 =0.25

Prob that both parents had aa and the child had aa = 0.253 = 0.015625

Hence conditional prob (parents both are aa/child has aa)

= 0.015625/0.25

= 0.0625

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