According to the question, a pair of dice has been thrown
So the number of elementary events in sample space will be $6^2=36$
n (S) = 36
By using the formula of probability, we get,
P (E) = favourable outcomes / total possible outcomes
(i) Let E be the event of getting sum less than 6
E = {(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (3,1) (3,2) (4,1)}
n (E) = 10
P (E) = n (E) / n (S)
= 10 / 36
= 5/18
(ii) Let E be the event of getting sum less than 7
E = {(1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (4,1) (4,2) (5,1)}
n (E) = 15
P (E) = n (E) / n (S)
= 15 / 36
= 5/12