Phenylketonuria (PKU) is a human hereditary disease resulting from the inability

Question

Phenylketonuria (PKU) is a human hereditary disease resulting from the inability of the body to process the chemical phenylalanine, which contained in the protein that we eat. PKU is caused by a autosomal recessive allele with simple Mendelian inheritance. A normal couple intends to have children but consult a genetic counselor because the man has a sister with PKU and the woman has a brother with PKU. There are no other known cases in their family. They want to know: 1. What is the probability that their first child would be normal? 2. What is the probability that their first two children would have PKU? 3. If they would like to have five children, what is the probability that all them would be normal?

Explanation / Answer

PKU: WT allele = P
Mutant allele = p
Both are autosomal recessive traits.
Genotype of the female's brother = pp
So, her parents, must carry atleast one mutant allele each (Assuming that they are homozygous recessive)
Genotype of the female = Pp
Similarly,
Genotype of the male's sister = pp
Genotype of the male = Pp
Parental cross: Pp X Pp
Gametes: (P) (p) X (P) (p)
Progeny:
PP = 1 = WT
Pp = 2 = Heterozygous normal
pp = 1 = Mutant

1. Probability for their first child to be normal = 3/4 = 0.75
2. Probability for the first child to be affected = 1/4
Probability for the second child to be affected = 1/4
Probability for both the childs to be affected = 1/16
3. Probability for the first child to be normal = 3/4
Probability for all the five childs to be normal = (3/4)^5 = 243/1024 = 0.237 = 23.7%

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