Question

(III.) Below is a pedigree for a family in which one member is hemophilic. A D (1.) Find the probability that individual A is a carrier (2.) Find the probability that individual C is a carrier (3.) Find the probability that individual D is a carrier (4.) Find the probability that individual B is a carrier Questions to think about Why would we never need to find the probability that a male is a carrier? In the real world, why would we never need to find the probability that an earning goals for this worksheet Determine genotypes from a pedigree Use Bayes formula in a real-world context 105

Answer 1

2)

Given, 1 A B 3 A

The abnormal hemophilia gene resides on the X chromosomes. A woman who carries the abnormal gene on one of her X chromosomes will develop symptoms of the disease.

However, a woman who carries the abnormal gene on one of her X chromosomes, but not on the other, is a carrier of the disease, but will not develop symptoms of the disease.

Of course a woman who carrier normal genes on both of her X chromosomes will not develop symptoms of the disease.

Every male has one X chromosome and one Y chromosomes. A male who carries the abnormal gene on his X chromosome will develop the symptoms of hemophilia, while a male who carries a normal gene on his X chromosome will not have hemophilia.

The first task is to determine what information the pedigree can provide regarding the individual C. Start by analyzing the males in the pedigree:

Based on the discussion given above, any male who is unaffected by hemophilia must have a normal gene on his X chromosome, and hence is not a carrier of the disease. Based on the given pedigree, the males I-1, II-1, II-5 and III-1 are all unaffected by hemophilia, and hence are not carriers of the disease.

On the other hand, the male III-4 is affected by hemophilia, so he must have an abnormal gane on his X chromosome.

Now that the males have all been analyzed, to determine more information about individual C, we need to analyze all of the females in her immediately family, which consists of her two sisters and her mother.

Start by analyzing her two sisters. The leftmost sister is B. Since B is unaffected by hemophilia, she must either have two normal genes, or one normal gene and one abnormal gene. In an attempt to determine which of these possibilities is true, examine her husband and son.

The portion of the pedigree consisting of the husband and son of B, along with B herself, is shown below:

1 TT

The son of B has one X chromosome and one Y chromosome. His Y chromosome must have come from his father (since his mother does not have any Y chromosomes), and his X chromosome must have therefore come from his mother B.

Since the son's X chromosome has the normal gene, and this chromosome came from the mother, we know that the mother has at least one normal gene. However, we already knew this information, so based on our analysis so far, the most information we can conclude is that B must either have two normal genes, or one normal gene and one abnormal gene. That is, she may or may not be a carrier.

The rightmost sister of C is II-4. The portion of the pedigree consisting of the husband and children of II-4, along with II-4 herself, is shown below:

Notice that II-4 has a son III-4 who is affected by hemophilia. The son therefore has an abnormal gene on his X chromosome. This abnormal gene must have come from his II-4, since his father II-5 gave him his Y chromosome. So the mother II-4 has at least one abnormal gene.

5 Scanned wILh CamScanner

Since II-4 is unaffected by hemophilia, she must have one normal gene and one abnormal gene. That is, she is a carrier.

Finally, focus on A, who is the mother of C. The portion of the pedigree consisting of A and her husband and daughters is shown below:

We know that the leftmost daughter B either has two normal genes, or one abnormal gene and one normal gene. On the other hand, the rightmost daughter II-4 is known to be a carrier, meaning she has one normal gene and one abnormal gene. The abnormal gene (which is on one of her X chromosomes) must have come from her mother A, beacuse her father's only X chromosome carriers the normal gene.

A I CS ScannedBwith CamScanner 4

Therefore, the mother A has at least one abnormal gene. And since she is not affected by hemophilia, she must also have at least one normal gene. So she is a carrier, meaning that she has one normal gene and one abnormal gene.

At this point, notice that, since the genotype of I-1 and B are known. Also, the genotype of C is independent of the genotypes of her siblings (and their families and offspring). Moreover, C has no offspring of her own. Therefore, the genotypes of C's parents are the only information that is needed to determine the probability that C is a carrier.

The father of C, who is I-1, carries a normal gene on his X chromosome, which he gives to C. On the other hand, the mother of C, who is A, carries the normal gene on one of her X chromosomes, and carries the abnormal gene on her other X chromosome.

If the mother gives her daughter the normal gene, the daughter will not be a carrier (since the father also gives the daughter a normal gene). If the mother gives her daughter the abnormal gene, then the daughter will be a carrier. Both of these possibilities are equally likely, so it follows that:

The probability is 1/2 that C is a carrier.

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