The six faces of a cube (die) are numbered as 1, 2, 3, 4, 5 and 6, and it is rolled once.
An outcome is the observed number on the top face. If the probability of getting an
odd number as an outcome is twice that of an even number, then the probability of
getting a number less than 3 is ________.
Options:
(A) 1
9
(B) 2
9
(C) 1
3
(D) 4
9
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2024 Q.31)**
**1. Governing Concept & Domain**:
This question evaluates **Engineering Mathematics** under *Section 1: Engineering Mathematics* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Engineering Mathematics.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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