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If two fair dice are rolled what is the probability that the total number of spots shown is equal to 6?
P(6) = 5/36 = 0.138888... ≈ 13.9%
When two fair dice are rolled, the sample space (all possible outcomes) has 36
equiprobable events:(1,1), (1,2), (1,3), (1,4), (1,5),(1,6), (2,1), (2,2), (2,3), (2,4),
(2,5), (2,6), (3,1), (3,2), (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).
There are 5 events where the sum of the dots of each die is equal to 6:
(1,5), (2,4), (3,3), (4,2), (5,1).
So in two fair dice are rolled the probability that the total number of spots shown is equal to 6 is, P(6) = 5/36 = 0.138888... ≈ 13.9%
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If two twelve side fair dice are rolled what it the probability that the total number of spots shown is equal to 5?
If two twelve side fair dice are rolled, there are 144 possible outcomes. Of those 144 outcomes, there are four (1-4, 2-3, 3-2, and 4-1) that add up to five, So the probability of rolling a sum of five is 4 in 144, or 1 in 36.
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