A die is thrown once. Find the probability of getting

(i) a prime number;

(ii) a number lying between 2 and 6;

(iii) an odd number.

In a single throw of dice.

Sample space = {1, 2, 3, 4, 5, 6}

No. of possible outcomes = 6

(i) Favourable outcomes (of getting a prime number) = 2, 3, 5.

No. of favourable outcomes = 3

P(getting a prime number)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

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

(ii) Numbers lying between 2 and 6 are 3, 4, 5.

No. of favourable outcomes = 3

P(getting a number lying between 2 and 6)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Hence, the probability of getting a number lying between 2 and 6 = $\dfrac{1}{2}$.

(iii) Favourable outcomes (of getting an odd number) = 1, 3, 5.

No. of favourable outcomes = 3

P(getting an odd number)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Hence, the probability of getting an odd number = $\dfrac{1}{2}$.