Two dice are thrown simultaneously, write all possible outcomes. Find :

(i) probability of getting same number on both the dice.

(ii) probability of getting a sum 7 on the uppermost faces of both the dice.

(i) Total number of possible outcomes = 36 (i.e., (1,1), (1,2), (1,3), (1,4), (1,5),……………(6,5), (6,6))

Number of favourable outcomes (Getting same number on both the dice) = 6 ((1,1), (2,2), (3,3), (4,4), (5,5), (6,6))

P(Getting same number on both the dice) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{6}{36}$

= $\dfrac{1}{6}$

Hence, the probability of getting same number on both the dice is $\dfrac{1}{6}$.

(ii) Total number of possible outcomes = 36 (i.e., (1,1), (1,2), (1,3), (1,4), (1,5),……………(6,5), (6,6))

Number of favourable outcomes (Getting a sum 7 on the uppermost faces of both the dice) = 6 ((1,6), (2,5), (3,4), (4,3), (5,2), (6,1))

P(Getting a sum 7 on the uppermost faces of both the dice) = $\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

= $\dfrac{6}{36}$

= $\dfrac{1}{6}$

Hence, the probability of getting a sum 7 on the uppermost faces of both the dice is $\dfrac{1}{6}$.