Two dice are thrown at the same time.

Two dice are thrown at the same time.                                                                                     [given]

So, total number of possible outcomes = 36

(i) We have, same number on both dice.

So, possible outcomes are (1,1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).

$\therefore$ Number of possible outcomes $=6$

Now, $\quad$ required probability $=\frac{6}{36}=\frac{1}{6}$

(ii) We have, different number on both dice.

So, number of possible outcomes

$=36$ - Number of possible outcomes for same number on both dice

$=36-6=30$

$\therefore$ Required probability $=\frac{30}{36}=\frac{5}{6}$