As we all know that,

A die is rolled one time, the possible outcomes are $1,2,3,4,5$, and $6$.

If two dice are rolled then possible outcomes are:

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

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

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

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

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

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

Hence, the total number of outcomes $=36$

(i)

The probability of getting a sum of $6$,

Favorable outcomes $=(1,5),(2,4),(3,3),(4,2),(5,1)$

Number of favorable outcomes $=5$

P(getting a sum of $6$) = Number of favorable outcomes/total number of Outcomes

$=5/36$

(ii)

The probability that getting two different digits,

Now we have to use formula to find out probability of getting two different digits

P(two different digits) $=1$  P(both digits are same)

Favorable outcomes for both digits are same $=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)$

Number of favorable outcomes $=6$

P(getting two different digits) $=1-(6/36)$

$=1–(1/6)$

$=(6–1)/6$

$=5/6$