Chapter 12, Problem 1TYU

A man with hemophilia (a recessive, sex-linked condition) has a daughter without the condition, who marries a man who does not have hemophilia. What is the probability that their daughter will have the condition? Their son? If they have four sons, that all will be affected?

Summary Introduction

To determine:

The probability that son will have the hemophilia condition, when a man with hemophilia (a recessive, sex-linked condition) has a daughter without hemophilia who marries a man who does not have hemophilia. Determine whether all the four sons will be affected or not.

Introduction:

Hemophilia is a sex-linked disorder, which impairs the blood-clotting mechanism in the affected individuals. Those individuals who receive the non-functional gene from their parents must have X-chromosome linked to recessive trait.

Explanation of Solution

Consider the genotypes of daughter as H and h. As the male suffers from the hemophilic condition, the disorder is linked with the male chromosomes XY. The disorder is recessive and sex-linked. Here, the male chromosomes are considered as Hh. The probability that the daughter will be hemophilic is zero.

The female has one wild type allele (H) and one recessive mutant allele (h).  The male has only wild-type allele and a Y chromosome. If the disorder is not linked with Y chromosome, then it is considered to be 0. The males received only one X chromosome, and hence, they have higher chances of carrying this disorder.

The sons have 50% chances of being affected by hemophilia. There is ½ probability that the sons are affected by the hemophilic condition.

Here, the Y chromosome does not contain hemophilia. Therefore, the hemophilic conditions are more dominant in sons.

As each son has a 50% chance of being affected by hemophilia, the probability of four sons is calculated as follows:

  $\begin{array}{l}=\left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)\\ =\frac{1}{16}\end{array}$

Here, the probability of all the sons who are affected is $\frac{1}{16}$ .

Conclusion

The man with hemophilia and his daughter and son in law without this disease and the probability of acquiring this disease in his granddaughter is about 0.  If he has a grandson, then it would be of ½ probability and in case if he has 4 grandsons, then it would be of 1/16 probability.