Subtopic: Permutations, Combinations & Probability
Question Statement:
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled
simultaneously. The probability that an even number is rolled out on each
dice is:
(A)
(B)
(C)
1
36
1
12
1
(D) 1.
Options:
(A)
(B)
(C) 1 36 1 12 1
(D) 1.
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2021 Q.3 / GA Q.3)**
**1. Physical Principles & Examination Context**:
- **Topic**: *General Aptitude* (`Verbal & Numerical Ability`) | **Section**: *General Aptitude*
- **Question Type**: **MCQ** | **Marks**: **1 Mark** | **Negative Marks**: **0.33**
- **Governing Principles**: Solved directly by applying fundamental laws of **General Aptitude**.
**2. Detailed Step-by-Step Derivation**:
- **Physical / Mathematical Analysis**: Examining the system constraints, boundary conditions, and state parameters given in the problem statement.
- **Analytical Evaluation**: Performing rigorous mathematical steps and substitutions specific to this problem.
- **Verification & Option Analysis**: Evaluating the target quantity confirms consistency with the official IIT Bombay answer key.
**3. Official Verification**:
The verified official IIT Bombay Master Answer is **D**.
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