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

(i) less than 3

(ii) greater than or equal to 4

(iii) less than 8

(iv) greater than 6

We know that,

In throwing a dice, total possible outcomes = {1, 2, 3, 4, 5, 6}

No. of favourable outcomes = 6.

(i) On a dice, numbers less than 3 are = {1, 2}

∴ No. of favourable outcomes = 2.

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

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

(ii) On a dice, numbers greater than or equal to 4 = {4, 5, 6}

∴ No. of favourable outcomes = 3.

P(getting a number greater than or equal to 4) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{6} = \dfrac{1}{2}$.

Hence, the probability of getting a number greater than or equal to 4 is $\dfrac{1}{2}$.

(iii) On a dice, numbers less than 8 = {1, 2, 3, 4, 5, 6}

∴ No. of favourable outcomes = 6.

P(getting a number less than 8) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{6}{6} = 1$.

Hence, the probability of getting a number less than 8 = 1.

(iv) On a dice, numbers greater than 6 = 0

∴ No. of favourable outcomes = 0.

P(getting a number greater than 6) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{6}$ = 0.

Hence, the probability of getting a number greater than 6 = 0.