In a single throw of a dice, find the probability of getting a number :

(i) greater than 4.

(ii) less than or equal to 4.

(iii) not greater than 4.

Here, the sample space = {1, 2, 3, 4, 5, 6}

So, No. of possible outcomes = 6

(i) No. greater than 4 = {5, 6}

∴ Number of favourable outcomes = 2

Thus, P(getting a no. greater than 4) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{2}{6} = \dfrac{1}{3}$.

Hence, the probability of getting a number greater than 4 = $\dfrac{1}{3}$.

(ii) No. less than or equal to 4 = {1, 2, 3, 4}

∴ Number of favourable outcomes = 4

Thus, P(getting a no. less than or equal to 4) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{6} = \dfrac{2}{3}$.

Hence, the probability of getting a number less than or equal to 4 = $\dfrac{2}{3}$.

(iii) Numbers not greater than 4 = {1, 2, 3, 4}

∴ Number of favourable outcomes = 4

Thus, P(getting no. not greater than 4) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{6} = \dfrac{2}{3}$.

Hence, the probability of getting a number not greater than 4 = $\dfrac{2}{3}$.