Question

If a fair die is rolled twice, what is the probability that the sum is at least 10?

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{1}{9}$
• D. $\frac{1}{4}$

Hint:

For probability with dice, list all favorable outcomes systematically to avoid missing pairs.

Answer 1

The Correct Option is B

A fair die has 6 faces, so two rolls give $6 \cdot 6 = 36$ possible outcomes.
We need the sum of the two rolls to be at least 10 (i.e., 10, 11, or 12).
List the favorable outcomes:
- 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 = $3 + 2 + 1 = 6$.
Probability:
\[ P(\text{sum} \geq 10) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6} \]
Thus, the correct answer is option (2).