GATE BT 2010 • Q13
MCQ • 1 Mark
Section 1: Engineering Mathematics
Probability and Statistics
Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
A culture of bacteria is infected with bacteriophage at a multiplicity of 0.3. The probability of a single cell infected with 3 phages is
Options:
-
(A) 0.9
-
(B) 0.27
-
(C) 0.009
-
(D) 0.027
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2010 Q.13)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: Biotechnology
- **Question Type**: **MCQ** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"A culture of bacteria is infected with bacteriophage at a muliplicity of 0.3. The probability of a
single cell infected with 3 phages is
(A)..."*
- **Option (D) [CORRECT]**: *"0.27
0.027"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"0.9"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"0.009"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **D**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.33 marks).
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