Two dice are rolled together. Find the probability of getting :

(i) a total of at least 10.

(ii) a multiple of 2 on one die and an odd number on the other die.

When two dice are thrown simultaneously;

Total number of possible outcomes = 6 × 6 = 36.

(i) For obtaining a sum of at least 10, the favourable outcomes are :

(4, 6), (5, 5), (5, 6), (6, 4), (6, 5) and (6, 6).

∴ No. of favourable outcomes = 6.

P(getting a total of at least 10) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{6}{36} = \dfrac{1}{6}$.

Hence, the probability of getting a total of at least 10 = $\dfrac{1}{6}$.

(ii) For obtaining a multiple of 2 on one die and an odd number on the other die, the favourable outcomes are :

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

∴ No. of favourable outcomes = 18.

P(getting a multiple of 2 on one die and an odd number on the other die) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{18}{36} = \dfrac{1}{2}$.

Hence, the probability of getting a multiple of 2 on one die and an odd number on the other die = $\dfrac{1}{2}$.