Understanding Haemophilia Inheritance and Probability

Haemophilia is a genetic disorder that affects blood clotting. It is an X-linked recessive trait. This means the gene responsible for haemophilia is located on the X chromosome, and two copies of the recessive allele (one on each X chromosome) are needed for a female to be affected, while only one copy on the single X chromosome is needed for a male to be affected.

Let's denote the allele for normal blood clotting as $\text{X}^\text{H}$ and the allele for haemophilia as $\text{X}^\text{h}$.

Determining Parental Genotypes for Haemophilia

We are given that the mother is a haemophilia carrier. A carrier female has one normal allele and one recessive haemophilia allele. Her genotype is therefore $\text{X}^\text{H}\text{X}^\text{h}$.

The father is normal. Since haemophilia is X-linked, a normal male has the normal allele on his X chromosome and a Y chromosome. His genotype is $\text{X}^\text{H}\text{Y}$.

Punnett Square Analysis for Offspring Probabilities

To find the probability of their children inheriting these traits, we can use a Punnett square. The mother can produce gametes with either the $\text{X}^\text{H}$ or the $\text{X}^\text{h}$ chromosome. The father can produce gametes with either the $\text{X}^\text{H}$ or the Y chromosome.

Analyzing the Possible Offspring

The Punnett square shows the four possible genotypes for the offspring, each with an equal probability of $1/4$ or 25%:

• $\text{X}^\text{H}\text{X}^\text{H}$: This is a female with two normal alleles. She is a normal daughter.
• $\text{X}^\text{H}\text{Y}$: This is a male with a normal allele on his X chromosome. He is a normal son.
• $\text{X}^\text{H}\text{X}^\text{h}$: This is a female with one normal and one haemophilia allele. She is a carrier daughter.
• $\text{X}^\text{h}\text{Y}$: This is a male with the haemophilia allele on his X chromosome. He is an affected son.

Calculating the Probability of a Haemophilia Carrier Daughter

From the analysis, the four possible outcomes are a normal daughter, a normal son, a carrier daughter, and an affected son. Each outcome has a $1/4$ probability.

The probability of having a carrier daughter among all possible offspring is $1/4$, which is 25%.

However, genetics problems sometimes ask for the probability within a specific sex. Let's look at the female offspring only:

• $\text{X}^\text{H}\text{X}^\text{H}$ (Normal daughter)
• $\text{X}^\text{H}\text{X}^\text{h}$ (Carrier daughter)

There are two possible outcomes for a daughter. Out of these two outcomes, one is a carrier daughter ($\text{X}^\text{H}\text{X}^\text{h}$).

Therefore, the probability of a daughter being a carrier is $1$ out of $2$, which is $1/2$ or 50%. Based on the provided options and common interpretations of such questions in exams aiming for the 50% answer, the question is likely asking for the probability of having a carrier daughter *among the female offspring*.

Thus, the probability of having a haemophilia carrier daughter in this scenario is 50%.

Revision Table: Haemophilia Inheritance Key Points

Additional Information: X-Linked Recessive Inheritance Patterns

• X-linked recessive traits are more common in males because they only have one X chromosome. If they inherit the recessive allele on that X, they will express the trait.
• Females have two X chromosomes. They must inherit two copies of the recessive allele (one on each X) to express the trait.
• Females with one normal allele and one recessive allele are carriers. They usually do not show symptoms but can pass the recessive allele to their children.
• Affected fathers pass the recessive allele to all their daughters, who will be carriers, but none to their sons (who inherit the Y chromosome).
• Carrier mothers have a 50% chance of passing the recessive allele to each child, regardless of sex. Sons who inherit the recessive allele will be affected, while daughters who inherit it will be carriers.