Probability of rolling a sum of 9 or a sum that is even from two number cubes is 11/18 Explanation: When a dice is rolled there are different ways in which 9. can be obtained, which are (3,6) or (4,5) or (5,4) or (6,3). 4 options. As in all there are 6⋅6=36 options, probability is 4/36 or 1/9.
For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 options, probability is 18/36 or 1/2.
Note that the two events (getting 9 or even sum) are mutually exclusive, the probabilities can be just added i.e. combined probability is 1/9+1/2=2+9/18i.e. 11/18
We see that the side provided is the hypotenuse and the side we are looking for is opposite to the angle provided. Thus, we will use sin since sin uses opposite/hypotenuse.
