Here are all 36 possible rolls with two dice:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6) 

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) 

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Since we are given that one of the numbers is a 1,
we eliminate all the rolls that do not contain a 1,
and leave only those that do:
The ones containing a 1 are across the top and along the
left side. There are 11 of them:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1)  

(3,1)  

(4,1)  

(5,1)  

(6,1) 

Of those 11, the only ones that have sum 4 are (1,3) and (3,1)

That's 2 out of 11.

Answer: 

Edwin