lf two dice are rolled, the probability that the sum of the faces is greater than 10 is__________
When 2 dice are rolled the sum of the two can be any number in the the set [2, 12]. It is greater than 10 if it is 11 or 12.
For the sum to be 11 or 12, one of the two dice that are rolled has to be 6, the other can be 5 or 6. If the first die turns up 6 the other can turn up 5 or 6 and if the first turns up 5 the other die has to turn up 6.
The probability of a die turning up 6 is 1/6 and that of a die turning up 5 is 1/6. This gives the probability of the sum being greater than 10 as (1/6)*(2/6) + (1/6)*(1/6) = 3/36 = 1/12
When two dice are rolled, there is a probability of 1/12 that the sum is greater than 10.
The size of the sample space (the total number of outcomes) is 36. (The first die can be any number from one to six, as can the second die so the total number of outcomes is 6*6=36 using the fundamental counting theorem.)
Of the 36 possibilities, only 3 create a sum greater than 10: (5,6),(6,5), and (6,6).
Thus the probability is 3/36=1/12.