Two fair six-sided dice are rolled simultaneously. Given that the sum of the numbers is greater than 8, what is the conditional probability that the numbers are equal?
Answer and explanation
Correct answer: D. 1/5
- Sum = 9: (3,6), (4,5), (5,4), (6,3) [4 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 outcomes with sum > 8 = 4 + 3 + 2 + 1 = 10 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 outcomes with sum > 8 = 4 + 3 + 2 + 1 = 10 outcomes.
- Step 1: Outcomes with sum > 8:
- Step 2: Outcomes among these where numbers are equal: (5,5) and (6,6) [2 outcomes].
- Step 3: P(Equal | Sum > 8) = 2 / 10 = 1/5.
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