A dice has 6 faces marked by the given numbers as shown below :

$\boxed{1} \quad \boxed{2} \quad \boxed{3} \quad \boxed{-1} \quad \boxed{-2} \quad \boxed{-3}$

The dice is thrown once. What is the probability of getting

(i) a positive integer ?

(ii) an integer greater than -3 ?

(iii) the smallest integer ?

Since, there are 6 faces in a dice.

∴ No. of possible outcomes = 6.

(i) Favourable outcomes for getting a positive integer are 1, 2, 3.

∴ No. of favourable outcomes = 3.

P(getting a positive integer) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Hence, the probability of getting a positive integer = $\dfrac{1}{2}$.

(ii) Favourable outcomes for getting an integer greater than -3 are -2, -1, 1, 2, 3.

∴ No. of favourable outcomes = 5.

P(getting an integer greater than -3)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{5}{6}$.

Hence, the probability of getting an integer greater than -3 = $\dfrac{5}{6}$.

(iii) Favourable outcomes for getting smallest integer is -3.

∴ No. of favourable outcomes = 1.

P(getting smallest integer) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{6}$.

Hence, the probability of getting smallest integer = $\dfrac{1}{6}$.