Phenylketonuria (PKU) is a disease that results from a recessive gene. Suppose that two unaffected parents produce a child with PKU. a. What is the probability that a sperm from the father will contain the PKU allele? b. What is the probability that an egg from the mother will contain the PKU allele? c. What is the probability that their next child will have PKU? d. What is the probability that their next child will be heterozygous for the PKU gene?
The Correct Answer and Explanation is :
Phenylketonuria (PKU) is caused by a recessive allele, meaning an individual must inherit two copies of the mutated gene (one from each parent) to express the disease. In the case of two unaffected parents who have a child with PKU, both parents must be carriers of the recessive allele (heterozygous).
a. Probability that a sperm from the father will contain the PKU allele:
Each parent has two alleles for each gene—one from each of their own parents. Since both parents are carriers (heterozygous, Pp), they carry one dominant normal allele (P) and one recessive PKU allele (p). When the father produces sperm, there is a 50% chance that a sperm will contain the p allele (the PKU allele) because he is Pp.
Thus, the probability is 50% or 1/2.
b. Probability that an egg from the mother will contain the PKU allele:
Similarly, the mother is also a carrier (Pp). When she produces eggs, there is a 50% chance that an egg will contain the p allele (the PKU allele).
Thus, the probability is also 50% or 1/2.
c. Probability that their next child will have PKU:
For a child to have PKU, they must inherit the p allele from both parents. Since each parent has a 50% chance of passing on the p allele, the possible combinations of alleles for the child are:
- PP (normal) – 25% chance
- Pp (carrier) – 50% chance
- pp (affected, with PKU) – 25% chance
Thus, the probability that the child will inherit PKU is 25% or 1/4.
d. Probability that their next child will be heterozygous for the PKU gene:
For the child to be heterozygous (Pp), they must inherit the P allele from one parent and the p allele from the other. There are two combinations that result in a heterozygous child: Pp or pP. Since the probability of each parent passing on the P allele is 50%, and the probability of the other parent passing on the p allele is also 50%, the probability of the child being heterozygous is:
50% (from the father) × 50% (from the mother) + 50% (from the mother) × 50% (from the father) = 50%.
Thus, the probability that their next child will be heterozygous is 50% or 1/2.