Question

Two dice are rolled together. The probability of getting a sum more than 9 is

• A. \(\dfrac{5}{6}\)
• B. \(\dfrac{1}{6}\)
• C. \(\dfrac{5}{18}\)
• D. \(\dfrac{1}{2}\)

Hint:

List all outcome pairs to count favorable ones, especially when dealing with two dice.

Answer 1

The Correct Option is B

Given:
Two dice are rolled together.
Find the probability that the sum of the numbers on the two dice is more than 9.

Step 1: Total possible outcomes
Each die has 6 faces.
Total outcomes when two dice are rolled = \(6 \times 6 = 36\).

Step 2: Find favorable outcomes (sum > 9)
Possible sums greater than 9 are 10, 11, and 12.
- Sum = 10: (4,6), (5,5), (6,4) → 3 outcomes
- Sum = 11: (5,6), (6,5) → 2 outcomes
- Sum = 12: (6,6) → 1 outcome
Total favorable outcomes = \(3 + 2 + 1 = 6\).

Step 3: Calculate probability
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6} \]

Final Answer:
\[ \boxed{\frac{1}{6}} \]