Two fair six-sided dice are rolled simultaneously. What is the probability that the sum of the numbers rolled is at least 10?
Answer and explanation
Correct answer: A. 1/6 (or 6/36)
- Step 1: Total possible outcomes when rolling two dice = 6 * 6 = 36 equiprobable outcomes.
- Step 2: We seek the outcomes where Sum >= 10:
- Step 3: Sum = 10: (4, 6), (5, 5), (6, 4) -> 3 outcomes.
- Step 4: Sum = 11: (5, 6), (6, 5) -> 2 outcomes.
- Step 5: Sum = 12: (6, 6) -> 1 outcome.
- Step 6: Total favorable outcomes = 3 + 2 + 1 = 6 outcomes.
- Step 7: Probability = 6 / 36 = 1 / 6.
Answer
1/6 (or 6/36).
Why not the others: '1/12 (or 3/36)' counts only sum = 10; '5/36' misses one combination; '7/36' includes sum = 9 incorrectly.
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