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: Determine the total number of outcomes.
When two dice are rolled, each die has 6 faces. Total outcomes \(= 6 \times 6 = 36\).
Step 2: Identify outcomes with sum greater than 10.
Sum > 10 means sum = 11 or sum = 12.
Step 3: List outcomes with sum = 11.
(5, 6) and (6, 5) - that gives 2 outcomes.
Step 4: List outcomes with sum = 12.
Only (6, 6) - that gives 1 outcome.
Step 5: Count favorable outcomes.
Total favorable outcomes \(= 2 + 1 = 3\).
Step 6: Calculate the probability.
\(P(\text{sum} > 10) = \frac{3}{36} = \frac{1}{12}\). This matches option 3.
\[ \boxed{\dfrac{1}{12}} \]