Question 1026962
Let (r1, r2) be the ordered pair where r1 is the result of the first roll, and r2 is the number in the second roll.
Clearly X = r1 + r2.
For P(E|X = 9), there are four possible ordered pairs satisfying X = 9, namely

(6,3), (5,4), (4,5), and (3,6).

Of these, (5,4) corresponds to the event that the first roll is 5.
Thus, P(E|X = 9) = 1/4.
___________________________________________
For P(E|X = 10), there are three possible ordered pairs satisfying X = 10, namely

(6,4), (5,5), (4,6).

Of these, (5,5) corresponds to the event that the first roll is 5.
Thus, P(E|X = 10) = 1/3.
___________________________________________
For P(E|X = 11), there are only two possible ordered pairs satisfying X = 1, namely

(6,5), and (5,6).

Of these two, (5,6) corresponds to the event that the first roll is 5.
Thus, P(E|X = 11) = 1/2.