Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
A disease is inherited by a child with a probability of 1/4. In a family of four children, what is the probability that at least one child is affected?
Options:
(A) 175/256
(B) 81/256
(C) 1/256
(D) 255/256
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2012 Q.40)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Engineering Mathematics
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"A disease is inherite d by a child with a probability of 1/4. In a family with two children, the
probability that exactly one sibling is affected by this disease is..."*
- **Option (B) [CORRECT]**: *"3/8"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"1/4"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"7/16"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"9/16
2012 BIOTECHNOLOGY - BT
BT 7/16"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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