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Assuming:

  • you are rolling two six-sided dice:
  • "greater than 5" does not include 5

Number of possible rolls = 36 (6x6)

28 rolls satisfy "at least one die shows a 4 or the sum of the dice is greater than 5":

(1, 4), (1, 5), (1, 6),

(2, 4), (2, 5), (2, 6),

(3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),

The probability that at least on die shows a 4 or that the sum of the dice is greater than 5 is 28/36, or 7/9, or approx. 77.8%

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Q: What is the probability that at least one die shows a 4 or that the sum of the dice is greater than 5?
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