A dice is thrown once. Find the probability of getting :

(i) an even number

(ii) a number between 3 and 8

(iii) an even number or a multiple of 3.

In a single throw of dice, the possible outcomes are {1, 2, 3, 4, 5, 6}.

∴ No. of possible outcomes = 6.

(i) Out of 1, 2, 3, 4, 5, 6, the even numbers are 2, 4, 6.

∴ No. of favourable outcomes = 3.

P(getting an even number) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

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

(ii) Out of 1, 2, 3, 4, 5, 6, the numbers between 3 and 8 are 4, 5, 6.

∴ No. of favourable outcomes = 3.

P(getting a number between 3 and 8) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Hence, the probability of getting a number between 3 and 8 = $\dfrac{1}{2}$.

(iii) Out of 1, 2, 3, 4, 5, 6, the numbers that are either an even number or a multiple of 3 are 2, 3, 4, 6.

∴ No. of favourable outcomes = 4.

P(getting either an even number or a multiple of 3) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{6} = \dfrac{2}{3}$.

Hence, the probability of getting either an even number or a multiple of 3 = $\dfrac{2}{3}$.