Mr. Stevan is suffering from hemophilia and cystic fibrosis. His father is heterozygous for cystic fibrosis. The probability of Stevan's sperm having recessive X-linked as well as autosomal allele is
(a) `1/4`
(b) `1/16`
(c) `1/2`
(d) `1/8`

Options

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

Answer

To solve the problem regarding Mr. Stevan's sperm having recessive X-linked and autosomal alleles, we can break it down step by step:

### Step 1: Understand the Genetic Disorders
- **Hemophilia** is an X-linked recessive disorder. This means that the gene responsible for hemophilia is located on the X chromosome, and a male (who has one X and one Y chromosome) will express the disorder if he has the recessive allele on his X chromosome.
- **Cystic fibrosis** is an autosomal recessive disorder. This means that the gene responsible for cystic fibrosis is located on one of the autosomes (non-sex chromosomes), and an individual must inherit two copies of the recessive allele (one from each parent) to express the disorder.

### Step 2: Determine Mr. Stevan's Genotype
- Since Mr. Stevan has hemophilia, his genotype for the X-linked gene is X^hY, where X^h represents the X chromosome with the hemophilia allele.
- For cystic fibrosis, since his father is heterozygous (C/c), Mr. Stevan must have inherited one recessive allele (c) from his father and one recessive allele (c) from his mother. Therefore, his genotype for cystic fibrosis is cc.

### Step 3: Analyze the Sperm's Alleles
- When Mr. Stevan produces sperm, he can pass on either his X or Y chromosome. The probability of passing on the X chromosome (which carries the hemophilia allele) is 1/2, and the probability of passing on the Y chromosome is also 1/2.
- For cystic fibrosis, since Mr. Stevan is homozygous recessive (cc), all of his sperm will carry the recessive allele (c) for cystic fibrosis.

### Step 4: Calculate the Combined Probability
- The probability of Mr. Stevan's sperm carrying the X-linked recessive allele (hemophilia) is 1/2.
- The probability of Mr. Stevan's sperm carrying the autosomal recessive allele (cystic fibrosis) is 1 (since all sperm will carry the recessive allele).
- To find the probability of having both the X-linked recessive allele and the autosomal recessive allele, we multiply the probabilities:
\[ P(X^h \text{ and } c) = P(X^h) \times P(c) = \frac{1}{2} \times 1 = \frac{1}{2} \]

### Step 5: Conclusion
- The probability of Mr. Stevan's sperm having both the recessive X-linked allele (hemophilia) and the autosomal recessive allele (cystic fibrosis) is **1/2**.

### Final Answer
- The correct option is **(c) 1/2**.

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