Answer:
P(X > 8) = 5/18
P(X mod 5 ≠ 0) = 29/36
Explanation:
You want various probabilities related to the sum of two dice.
Greater than 8
Please refer to the attached chart of possible outcomes. There are 4 ways to roll a 9, 3 ways to roll a 10, 2 ways to roll 11, and one way to roll 12. That means there are 4+3+2+1 = 10 ways to roll a number greater than 8.
P(X > 8) = 10/36 = 5/18
Not divisible by 5
It is easier to count results that are divisible by 5. Then the difference between that number and 36 will be the number of outcomes not divisible by 5.
5 can be rolled 4 ways, and 10 can be rolled 3 ways. A total of 4+3 = 7 of the 36 outcomes are divisible by 5. That means 36 -7 = 29 are not divisible by 5.
P(X not divisible by 5) = 29/36
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