In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents
respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a
randomly drawn autocomponent from the combined lo t is found defective, what is the probability
that it was manufactured by M2?
(A) 0.35 (B) 0.45 (C) 0.5 (D) 0.4
Options:
(A) Q.35
(B) Q.45
(C) Q.5
(D) Q.4
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2013 Q.62)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: GA
- **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: *"In a factory, two machines M1 and M2 manufacture 60% and 40% of the autocomponents
respectively. Out of the total production, 2% of M1 and 3% of M2 are found to be defective. If a
randomly drawn autocomponent from the ..."*
- **Option (C) [CORRECT]**: *"0.5"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"0.35"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (B) [INCORRECT]**: *"0.45"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"0.4"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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