A couple comes in for counseling who already had one child who died from Tay-Sac

Question

A couple comes in for counseling who already had one child who died from Tay-Sachs. The woman is now at an early stage of pregnancy with their second child and would do anything to avoid another baby having this disease. After meeting with them and obtaining a family history, you set up another appointment to tell them your results.

a. What are the chances that this next child will also be affected?

b. Between appointments, the woman confides to you that her husband is not the true father of the child she is pregnant with. Does this increase, decrease, or leave unchanged, the likelihood that this child will have Tay-Sachs? Explain.

c. If the biological father is an Ashkenazi Jew, what will be the chances of the child being affected?

Explanation / Answer

a. This is an independent event, that is, the probability of a second child having the disease is independent of the condition of the first child. Therefore, the probability is 0.25. The disease is autosomal recessive, which means two mutant alleles must be inherited from both the parents. Consider both the parents are carriers, and the probability of inheritance is 1/4 or 0.25. But this is an independent event and is not affected by the previous event or pregnancy, so the probabilty of second child too being infected is 0.25.

b. If the husband is not the true father, and the true father is not a carrier, then the chances of baby getting infected is 0. Since the true father is not a carrrier, he bares no mutant allele and there is no inheritance of the mutant allele. On the other hand, if the true father also is a carrier, then the same probability of 0.25 is there for the child to inherit the disease.

c. The incidence of Tay-sachs in Ashkenazi jews is that 1 out of 30 is a carrier. That is, the probabilty tha the child inherites the allele from the pather is 0.0165.

One out of 30 is a carrier, so the probability that the father is a carrier is 0.033. The probability that the mutant allele is passed on to the offspring is 0.5 X 0.033 = 0.0165. The probability that the mutant allele is inherited from mother is 0.5.

The probability that the child inherits both the mutant alleles is 0.5 X 0.0165 = 0.008. The chances are very rare.

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