Question Statement
Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the two numbers shown is equal to 8? (Enter your answer as a fraction in simplest form as $A/B$, e.g., if answer is 5/36, enter 5/36)
Step-by-Step KaTeX Derivation & Detailed Explanation
### Step-by-Step Derivation & Verification: 1. **Total Sample Space Size**: Rolling two fair dice yields: $n(S) = 6 \times 6 = 36$ 2. **Favorable Events for Sum $= 8$**: $E = \{(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)\}$ $n(E) = 5$ 3. **Probability Evaluation**: $P(E) = \frac{n(E)}{n(S)} = \frac{5}{36}$ 4. **Official Fractional Form**: 5/36 (or decimal 0.14).