Two number cubes are rolled.
(a) list the sample space.
(b)what is the probability, as a simplified fraction, that the sum of the numbers is 4 or that the sum of the numbers is greater than 9? show your work.

The sample space is the set of the 36 possible couples:

So, we have

As for the probability of rolling a sum greater than 9, just count how many cases satisfy the request, and divide the number of cases by the cardinality of the sample space: the good rolls are

So, 10 out of 36 rolls are good, leading to a probability of