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If you roll two fair six-sided dice, what is the probability that the sum is 9 or higher?

If you roll two fair six-sided dice, what is the probability that the sum is 99 or higher?

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Full solution

Q. If you roll two fair six-sided dice, what is the probability that the sum is 99 or higher?
  1. Count Total Outcomes: Count the total number of possible outcomes for rolling two dice. Each die has 66 faces, so the total number of outcomes is 6×6=366 \times 6 = 36.
  2. Find Sum 99 or Higher: Find the number of outcomes where the sum is 99 or higher.\newlineThe pairs that sum to 99 or more are: (3,6)(3,6), (4,5)(4,5), (4,6)(4,6), (5,4)(5,4), (5,5)(5,5), (5,6)(5,6), (6,3)(6,3), 9900, 9911, and 9922.\newlineThat's 9933 pairs, but wait, I made a mistake, I missed some pairs.

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