Take two long dice (rectangular parallelepiped), each having four rectangular faces
labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces
and has 1/4 probability of landing on any of the four rectangular faces. The label on
the top face of the dice is the score of the throw.
If thrown together, what is the probability of getting the sum of the two long dice
scores greater than 11?
Options:
(A) 3/8
(B) 1/8
(C) 1/16
(D) 3/16
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.5)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Quantitative & Analytical Aptitude:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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