Question 1113047: A pair of dice is rolled. What is the probability of getting a sum greater than 6?
Answer by math_helper(2461)   (Show Source):
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Since the number of outcomes is small, we can enumerate the possible outcomes as a table:
1 2 3 4 5 6
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1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
You can see there are 36 outcomes and everything on the diagonal consisting of 7's and down to the right is greater than 6. That's 6+5+4+3+2+1=21, out of 36 outcomes, so Pr(dice total > 6) = 21/36 = 7/12.
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Another approach:
P(first die is a 6 and 2nd die is ANY value) = 1/6 = 6/36
+ P(first die is a 5 and 2nd is 2 or more) = (1/6)(5/6) = 5/36
+ P(first die is a 4 and 2nd is 3 or more) = (1/6)(4/6) = 4/36
+ P(first die is a 3 and 2nd is 4 or more) = (1/6)(3/6) = 3/36
+ P(first die is a 2 and 2nd is 5 or more) = (1/6)(2/6) = 2/36
+ P(first die is a 1 and 2nd is 6) = (1/6)(1/6) = 1/36
Adding these up gives (6+5+4+3+2+1)/36 = 21/36 = 7/12
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