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.

Answer:When two number cubes  are rolled,Sample space= Total Possible outcome {11,22,33,44,55,66,12,21,13,31,14,41,15,51,16,61,23,32,24,42,25,52,26,62,34,43,35,53,36,63,45,54,46,64,56,65}=36Probability of an event = \frac{\text{Total favorable outcome}}{\text{Total possible outcome}}Sum of 4 is obtained when ={13,31,22}=3Probability of getting 4 when 2 number cubes are rolled= \frac{3}{36}=\frac{1}{12}Sum of the numbers is greater than 9= 10, 11,12={55,64,46,56,65,66}=6Probability of getting(Sum of the numbers is greater than 9)=\frac{6}{36}=\frac{1}{6}