An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable. Of X's shock absorbers, 96% are reliable.
Of Y's shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y
is
(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720
Options:
(A) Q.288
(B) Q.334
(C) Q.667
(D) Q.720
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2012 Q.64)**
**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: *"An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the qu..."*
- **Option (B) [CORRECT]**: *"0.334"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"0.288"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"0.667"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"0.720"* 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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