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

(i) 5

(ii) 8

(iii) a number less than 8

(iv) a prime number.

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

∴ No. of possible outcomes = 6.

(i) No. of favourable outcomes (for getting a 5) = 1

P(getting a 5) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{6}$.

Hence, the probability of getting a 5 = $\dfrac{1}{6}$.

(ii) Since, no face as number 8 written on it, there is no outcome favourable to 8.

∴ No. of favourable outcomes = 0.

P(getting a number 8) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{6}$ = 0.

Hence, the probability of getting 8 = 0.

(iii) Out of 1, 2, 3, 4, 5, 6, the numbers less than 8 are 1, 2, 3, 4, 5 and 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) Out of 1, 2, 3, 4, 5, 6, the prime numbers are 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 = $\dfrac{1}{2}$.