A pair of standard dice is rolled. Find the probability that the sum of the two dice is less than 13.
To find the probability that the sum of the two dice is less than 13, we need to determine all the possible outcomes in which the sum is less than 13.
There are a total of 36 possible outcomes when rolling a pair of dice, because each die has 6 sides and there are 6 possible outcomes for each roll.
These outcomes include:
(1,1), (1,2), (1,3), ..., (1,6)
(2,1), (2,2), (2,3), ..., (2,6)
...
(6,1), (6,2), (6,3), ..., (6,6)
Out of these 36 outcomes, there is only one outcome where the sum is equal to 13: (6,6).
Therefore, the probability that the sum of the two dice is less than 13 is:
(36 - 1) / 36 = 35 / 36
So, the probability is 35/36 that the sum of the two dice is less than 13.