Mr. steven is suffering from haemophilia and cystic fibrosis . His father is hetrozygous for cystic fibrosis . The probability of Stavan's sperm having recessive X linked as well as autosomal allele is

Options

A. `(1)/(4)`
B. `(1)/(16)`
C. `(1)/(2)`
D. `(1)/(8)`

Answer

To solve the problem, we need to analyze the genetic conditions of Mr. Steven and his father, and then calculate the probability of his sperm carrying both a recessive X-linked allele (for hemophilia) and a recessive autosomal allele (for cystic fibrosis).

### Step-by-Step Solution:

1. **Identify the Genetic Disorders**:
- Hemophilia is an X-linked recessive disorder.
- Cystic fibrosis is an autosomal recessive disorder.

2. **Determine Mr. Steven's Genotype**:
- Since Mr. Steven has hemophilia, he must have the genotype X^hY (where X^h represents the X chromosome with the hemophilia allele).
- Since he also has cystic fibrosis, he must have the genotype aa (where 'a' represents the recessive allele for cystic fibrosis).

3. **Identify the Father's Genotype**:
- Mr. Steven's father is heterozygous for cystic fibrosis, meaning his genotype is Aa (where 'A' is the normal allele and 'a' is the cystic fibrosis allele).
- The father’s genotype for hemophilia is not directly given, but since he is the father of Mr. Steven who has hemophilia, he must have a normal X chromosome (X^H) and a Y chromosome (X^HY).

4. **Gamete Formation**:
- Mr. Steven can produce two types of gametes for his X-linked trait: X^h (with hemophilia) and Y (without hemophilia).
- For the cystic fibrosis trait, he can produce gametes with the recessive allele 'a' (for cystic fibrosis).

5. **Probability Calculation**:
- The probability of Mr. Steven's sperm carrying the X^h allele (for hemophilia) is 1/2 (since he can either pass on X^h or Y).
- The probability of his sperm carrying the recessive allele 'a' (for cystic fibrosis) is also 1/2 (since he can either pass on 'a' or 'A').

6. **Combined Probability**:
- Since these two events are independent (the inheritance of the X-linked trait does not affect the inheritance of the autosomal trait), we multiply the probabilities:
\[ P(X^h \text{ and } a) = P(X^h) \times P(a) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

### Final Answer:
The probability of Mr. Steven's sperm having both a recessive X-linked allele (for hemophilia) and a recessive autosomal allele (for cystic fibrosis) is **1/4**.

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