When rolling a dice two times, what is the probability of having a number greater that 3?

Let x or y be the number coming up when you throw a dice. x = {1,2,3,4,5,6) and y = (1,2,3,4,5,6}. Probabilty of obtaining a number greater than 3, or  P(x+y >3) =1 -  P(x+y < =3 ).

Now x+y  could be (1,1), (1,2),.....(6,6) in 36 ways.

x+y <=3 could be in one of the (1,1), (1,2) , (2,1) 3 ways. Therefore, P(x+y <= 3) = 3/36. =1/12.

Therefore, P(x+y >= 3) = 1 - P(x+y <=3) = 1 -1/12 = 11/12.