Answer:
[tex]\frac{1}{8}[/tex]
Explanation:
From the question: Duchenne muscular dystrophy is an X-linked recessive disease.
Now for an X-linked recessive disorder to be affected by a male individual; it only requires the presence of only one copy of the recessive allele of the disease to be present BUT in a female individual. both copies of the recessive allele must be present.
Let the X-linked recessive disease(i.e Duchenne muscular dystrophy) be = (ⁿ)
However, we are told that the couples are normal and are unaffected. Therefore;
the male partner (XY) will be: [tex]X^NY[/tex]
the female partner (XY) will be: [tex]X^NX^N[/tex]
Similarly, the question proceeds by telling us that: the woman's brother has the disease.
Definitely, it's possible that this unaffected woman is a carrier of the disease.
So, if she is a carrier; we have her traits to be: [tex]X^NX^n[/tex]
NOW, if a cross exist between these couples; we have
[tex]X^NY[/tex] × [tex]X^NX^n[/tex]
[tex]X^N[/tex] [tex]Y[/tex]
[tex]X^N[/tex] [tex]X^NX^N[/tex] [tex]X^NY[/tex]
[tex]X^n[/tex] [tex]X^NX^n[/tex] [tex]X^nY[/tex]
So, we have offspring as follows:
[tex]X^NX^N[/tex] = normal unaffected female
[tex]X^NY[/tex] = normal unaffected male
[tex]X^NX^n[/tex] = female carrier for the Duchenne muscular dystrophy disease
[tex]X^nY[/tex] = affected male with the Duchenne muscular dystrophy disease
So, the probability of the child to be affected with the disease = [tex]\frac{1}{4}[/tex]
Also, the probability that the first child will be a male or a female = [tex]\frac{1}{2}[/tex]
∴
the probability that the couple’s first child will be affected = [tex]\frac{1}{4}*\frac{1}{2}[/tex]
=[tex]\frac{1}{8}[/tex]
