Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
Two fair six-sided dice, with sides numbered 1 to 6, are thrown once. The
probability of getting 7 as the sum of the numbers on the top side of the
dice is _____________.
(Round off to two decimal places)
Official Answer Key:
0.16 to 0.18
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2025 Q.35)**
**1. Governing Concept & Definition**:
- **Topic**: Probability & Discrete Sample Spaces
- In throwing two fair six-sided dice, the total number of equally likely outcomes in the sample space $S$ is:
$n(S) = 6 \times 6 = 36$
- The probability of an event $E$ is:
$P(E) = \frac{n(E)}{n(S)}$
**2. Detailed Step-by-Step Calculation**:
- **Event $E$**: Sum of the numbers on the two dice equals 7.
- **Favorable Outcomes**:
$(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)$
- **Number of Favorable Outcomes**:
$n(E) = 6$
- **Probability Calculation**:
$P(E) = \frac{6}{36} = \frac{1}{6} \approx 0.1667$
**3. Final Answer**:
- **Calculated Value**: **0.17**
- **Official GATE Accepted Range**: **0.16 to 0.18**
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