A fair die is rolled repeatedly. The probability that the cumulative sum is at least 17 in the third trial is
Question and options
A fair die is rolled repeatedly. The probability that the cumulative sum is at least 17 in the third trial is
Answer and explanation
Correct answer: A - \(\frac{1}{54}\)
Two rolls give at most 12, so the sum first reaches >= 17 at the third roll iff the three-roll sum is >= 17: (6,6,6) and the 3 arrangements of (6,6,5), i.e. 4 of 216 outcomes = 1/54.
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