Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
A disease-associated allele shows X-linked recessive inheritance. If the mother is a
carrier of the disease, the father is genetically normal and the child born is a son,
then the probability that he is born with the disease is _______. (rounded off to one
decimal place)
Official Answer Key:
0.5 to 0.5
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.64)**
**1. Governing Concept & Definition**:
- **Topic**: Human Genetics & X-Linked Recessive Inheritance
- Let $X^A$ denote the normal allele and $X^a$ denote the disease-associated recessive allele.
- Carrier mother: $X^A X^a$
- Unaffected father: $X^A Y$
**2. Detailed Step-by-Step Calculation**:
- **Mating**: $X^A X^a \times X^A Y$
- **Offspring Genotypes**:
- Daughters:
- $X^A X^A$ (Normal female)
- $X^A X^a$ (Carrier female)
- Sons:
- $X^A Y$ (Normal male)
- $X^a Y$ (Affected male)
- **Question Condition**: Probability that a son born to this couple is affected:
$\text{Among sons: } P(X^a Y) = \frac{1}{2} = 0.5$
**3. Final Answer**:
- **Calculated Value**: **0.5**
- **Official GATE Accepted Range**: **0.5 to 0.5**
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