4.3 Problem Set 3: Examples using X-linked traits

1. Hemophilia is an X-linked recessive disease. We'll refer to the normal allele as Xh+, and the mutant allele as Xh. A woman with genotype Xh+/Xh marries a man with genotype Xh+/Y. They have four sons and two daughters.
a. On average, how many of the sons will have hemophilia?
b. On average, how many of the daughters will have hemophilia?
c. On average, how many of the daughters will be carriers for the hemophilia allele?
d. One of the daughters marries a man with genotype Xh+/Y. She has two sons and two daughters. One of her sons has hemophilia but neither of the daughters does. What was the mother's genotype?

2. Color blindness is also a recessive X-linked gene. Let's denote the normal and mutant alleles as Xb+ and Xb respectively. A woman with genotype Xb+/Xb marries a man of genotype Xb/Y. They have four sons and two daughters.
a. On average, how many of the sons will be color blind?
b. On average, how many of the daughters will be color blind?
c. On average, how many of the daughters will be carriers for the Xb allele?

3. The Xg blood group is an X-linked trait. Having the Xg+ allele for the Xg-positive blood type is dominant to having the Xg allele that doesn't produce this blood type. If a man who is Xg+/Y marries a woman who is Xg/Xg, what percentage of their sons will have the Xg positive blood type? What percentage of their daughters will have it?

4. For the X-linked hemophilia gene, the frequency of the normal allele is 0.95 and the frequency of the mutant allele is 0.05. Keeping in mind the difference in how X-linked genes affect the sexes, what is the probability that a man will have hemophilia? And a woman?
(Note: this hemophilia allele frequency is way too high, I think!!)

5. A phenotypically normal woman of unknown genotype for the hemophilia gene, marries a normal man of genotype Xh+/Y. Using the same allele frequencies as before:
(a) What is the probability that their child has hemophilia?
(b) What is the probability that their child is a carrier for hemophilia?
(c) What is the probability that their child is normal and not a carrier for hemophilia?

6. A man who is color-blind and has genotype Xb/Y, marries a woman of normal phenotype and unknown genotype. The frequency of the normal color-blindness allele (Xb+) is 0.8, and of the mutant color-blindness allele is 0.2.
(Note: again the allele frequency is too high!!)
Remembering that this disease is X-linked:
(a) What is the probability that their child is color-blind?
(b) What is the probability that their child is a carrier?
(c) What is the probability that their child is phenotypically normal? (that is, not color blind).