Question

The probability of getting sum greater than 10, when two dice are rolled together, is

• A. \(\frac{1}{9}\)
• B. \(\frac{1}{18}\)
• C. \(\frac{1}{12}\)
• D. 1

Hint:

To quickly count outcomes for dice sums: - Maximum possible sum is 12, which can only happen in 1 way: \((6, 6)\).
- A sum of 11 can happen in 2 ways: \((5, 6)\) and \((6, 5)\).
Summing these gives exactly 3 favorable outcomes out of 36.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The experiment consists of rolling two fair six-sided dice simultaneously. We need to find the probability that the sum of the numbers appearing on top of both dice is strictly greater than 10 (i.e., sum is 11 or 12).

Step 2: Key Formula or Approach: 1. The probability of an event \(E\) is given by: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] 2. When two dice are rolled, the total number of outcomes is: \[ 6 \times 6 = 36 \] 3. Favorable outcomes are pairs \((x, y)\) such that \(x + y \gt 10\).

Step 3: Detailed Explanation:
1. List all possible outcomes of rolling two dice: There are 36 possible outcomes, represented as pairs \((x, y)\) where \(x, y \in \{1, 2, 3, 4, 5, 6\}\).
2. Identify outcomes where the sum is greater than 10 (i.e., \(x + y = 11\) or \(x + y = 12\)): - For a sum of 11, the possible outcomes are: \[ (5, 6), (6, 5) \] - For a sum of 12, the only possible outcome is: \[ (6, 6) \] 3. Count the total number of favorable outcomes: Favorable outcomes are \((5, 6)\), \((6, 5)\), and \((6, 6)\). \[ \text{Number of favorable outcomes} = 3 \] 4. Calculate the probability: \[ P(\text{sum} \gt 10) = \frac{3}{36} = \frac{1}{12} \]

Step 4: Final Answer:
The probability of getting a sum greater than 10 is \(\frac{1}{12}\).
Therefore, the correct option is (C).