The gene for haemophilia (the inability of blood to clot) produces no
symptom in females, but a female who carries the gene will pass it on
to each of her children independently with probability ½ in each case.
Assume throughout this question that males with haemophilia
(haemophiliacs) do not marry or have children.

Mrs Smith is expecting her first child (a son), and it is known that
Mrs Smith's maternal uncle (the only brother of Mrs Smith's mother) is
a haemophiliac. Explain clearly why, in the light of this information,
the probability that Mrs Smith's son will be a haemophiliac is 1/8.

What would be the probability if instead it is known that Mrs Smith's
mother has four brothers, only one of whom is a haemophiliac?

Thanks!

hoolash@gmail.com wrote:
The gene for haemophilia (the inability of blood to clot) produces no
symptom in females, but a female who carries the gene will pass it on
to each of her children independently with probability ½ in each case.
Assume throughout this question that males with haemophilia
(haemophiliacs) do not marry or have children.

Mrs Smith is expecting her first child (a son), and it is known that
Mrs Smith's maternal uncle (the only brother of Mrs Smith's mother) is
a haemophiliac. Explain clearly why, in the light of this information,
the probability that Mrs Smith's son will be a haemophiliac is 1/8.

What would be the probability if instead it is known that Mrs Smith's
mother has four brothers, only one of whom is a haemophiliac?

Mrs Smith's Mother's Mother must be haemophiliac.
I think you mean that she is a carrier, not a haemophiliac.

So Mrs Smith's Mother carries the gene with prob 1/2.

Mrs Smith carries gene with prob 1/2 * 1/2 = 1/4.

Mrs Smith passes on gene with prob 1/4/* 1/2 = 1/8.



The probability remains the same if only one of Mrs Smith's mother's
brothers is a haemophiliac. This is because Mrs Smith's mother is
haemophiliac if any of them are haemophiliac hence the odds don't change.