Consider a woman whose brother is afflicted with hemophilia, which implies that the woman's mother has the hemophilia gene on one of her two X chromosomes. Thus there is a 50-50 chance that the woman's mother has passed on the bad gene to her. The woman has two sons, each of whom will independents inherit the gene from one of her two chromosomes. If the woman herself has a bad gene, there is a 50-50 chance she will pass this on to a son. Suppose that neither of her two sons is afflicted with hemophilia. What then is the probability that the woman is indeed the carrier of the hemophilia gene? What is the probability if she had a third son who also is not afflicted?

Question

Mathematics

Talan Compton

9 June, 00:19

Consider a woman whose brother is afflicted with hemophilia, which implies that the woman's mother has the hemophilia gene on one of her two X chromosomes. Thus there is a 50-50 chance that the woman's mother has passed on the bad gene to her. The woman has two sons, each of whom will independents inherit the gene from one of her two chromosomes. If the woman herself has a bad gene, there is a 50-50 chance she will pass this on to a son. Suppose that neither of her two sons is afflicted with hemophilia. What then is the probability that the woman is indeed the carrier of the hemophilia gene? What is the probability if she had a third son who also is not afflicted?

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Answers (1)

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Ada Rogers · Answer 1

33.33% and 25%

Step-by-step explanation:

If the woman has a 50-50 chance to pass on the disease to her children, then 1 out of 2 children may have the disease.

As she has two children and none of them have the disease, this reduces the chances that the woman is the carrier of the hemophilia gene to 1 out of 3, that is, 1/3 = 0.3333 or 33.33%.

After having a third son without the disease, the chances reduce to 1 out of 4, or ¼ = 0.25 = 25%

In this case the chances that the woman is the carrier of the hemophilia gene is 25%