A die is rolled twice. what is the probability that the sum of the rolls is less than 4 given that one of the rolls is a 1?

First let's see in how many way we can get a sum <4

well first role is 1

second role can be 1, 2, 3, 4, 5, 6

we can have this combinations

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

out of all this only 1,1 and 1,2 add up to less than 4

so 2/6=1/3