Question

What is the probability that the first son of a woman whose brother is affected will be affected? What is the probability that the second son of a woman whose brother is affected will be affected if her first son was affected?

Duchenne muscular dystrophy (DMD) is cause by a relatively rare X-linked recessive allele. It causes progressive muscular wasting, and usually leads to death before age 20.

Answer 1

`P("first son has DMD")=25%`
`P("second son has DMD"|"first son has DMD")=50%`

Explanation:

If a woman's brother has DMD then the woman's mother is a carrier of the gene. The woman will get half of her chromosomes from her mother; so there is a `50%` chance that the woman will inherit the gene.

If the woman has a son, he will inherit half of his chromosomes from his mother; so there would be a `50%` chance if his mother was a carrier that he would have the defective gene.

Therefore if a woman has a brother with DMD there is a
`50%XX50%=25%` chance that her (first) son will have DMD.

If the woman's first son (or any son) has DMD then the woman must be a carrier and there is a `50%` chance that any other son would have DMD.