In the question it specifies that we are looking for the probobility that a triangle can exist with side lengths of 1, x and y.

We do know that x and y can be either 0, 1, 2 or 3. We can list that all out:

1,0,0

1,0,1

1,0,2

1,0,3

1,1,0

1,1,1

1,1,2

1,1,3

1,2,0

1,2,1

1,2,2

1,3,0

1,3,1

1,3,2

1,3,3

This gives us a 50/50 chance or 1/2 chance that a triangle with 1,x and y can exists.

Btw I am looking at the problem now and it says the answer is 1/2.

This is just my attempt to explain this but if you see issues with my solving of this problem please point them out.

If you are just here for the answer it is: 1/2