Question

Alexei Romanov, the only son of Tsar Nicholas II of Russia, suffered from the genetic disease hemophilia. Hemophilia is inherited via the X-chromosome: women have two versions of the allele, one inherited from each parent; while men have one, inherited from the mother. A person with at least one version of the dominant allele, H, does not have the disease, while a person who has only the recessive allele, h, has the disease. That is, women may have alleles HH (no hemophilia), Hh (carrier of hemophilia), or hh (hemophilia); men may have H (no hemophilia) or h (hemophilia). Neither Tsar Nicholas nor his wife Tsarina Alexandra had hemophilia.

(a) Given that Alexei had hemophilia, what is the probability that his sister Anastasia was a carrier?
(b) During the Bolshevik revolution, the entire Romanov family was assassinated by revolutionaries; however, rumors abounded that some of the women had escaped. Several years later, a woman named Anna Anderson surfaced, claiming to be Anastasia. According to her story, Anna had escaped from Russia, married, and had a son, whom she left in an orphanage. Suppose it was initially believed to be only 5% likely that Anna was truly Anastasia, and suppose that 1%ofmen at the time had hemophilia. If Anna’s son were found to have hemophilia, how would that change the probability that Anna was Anastasia?
(c) If instead, Anna’s son was found not to have hemophilia, what would be the updated probability that Anna was Anastasia?

Answer 1

As given n question, Alexi is son of Tasar Nicholas II, and is a Haemophilic.

Haemophilia is X-linked Recessive disease and dominant allele = H --- non-haemophilic ; while h = recessive allele ---- Haemophilic. So, a person to be Haemophilic must be Homozygous Recessive or hh. As the disease is due to X-chromosome so represented by XH or Xh.

Female Genotypes --- XH XH --- non-haemophilic ;. XH Xh --- non-haemophilic but carrier; Xh Xh ----Haemophilic.

Male Genotypes -------- XH Y ---- non-haemophilic ; Xh Y ----- Haemophilic ; males can't be carreir due to only one X-chromosome In them.

given that Neither Tasar nor his wife had Haemophilia. So, Genotype of Tasar is confirmed = XH Y. But the Genotype of his wife can be = XH XH or XH Xh. But it is given that Alexi, son is Haemophilic. So, the son, Alexi to be Haemophilic mother must have a Haemophilic Allele. So, it conclude that the Genotype of Tsar Nicholas II's wife is = XH Xh.

Ans a) the Probability that sister of Alexi, Anastasia is a carrier.

Genotypes of parents Tasr and his wife are ---

Tsar = XH Y ; wife = XH Xh. Cross them,

	XH	Xh
XH	XH XH	XH Xh
Y	XH Y	Xh Y

Green color --- non-haemophilic, not carrier

Yellow color --- non-haemophilic but carrier

Red color ---- Haemophilic

Anastasia is female and the possible Genotypes of female offsprings are = XH XH and XH Xh

Total female = 2

Carrier = 1 ( XH Xh)

Probability of Anastasia being a carreir = 1/2

ans b ) now given Anna claims to be Anastasia so, her possible Genotypes are = XH XH or XH Xh

Her story is believed to be = 5% or 5/100

And men are Haemophilic by = 1% or 1/100

If Anna son was Haemophilic. Then her Probability to be Anastasia =

Probability of believing her story * her probability of being a carrier ( as she have a Haemophilic son)

= 5/100 * 1/2 (Probability of Anastasia being a carrier and transferred h to his son)

= 1/20 * 1/2

= 1/40

Ans c) if Anna's son was not found Haemophilic. Then her probability of being Anastasia =

Probability of believing her story * her probability of not not being a carrier ( Anastasia was not a carrier of Haemophilia )

= 5/100 * 1/2

= 1/20 * 1/2

= 1/40

Probability Anastasia was a carreir but did not pass h to his son making him non-haemophilic ( 1/2)

5/100 * 1/2 = 1/40

P = 1/40 * 1/40

=1/80