A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (shown in the adjoining figure) and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

Sample space = {1, 2, 3, 4, 5, 6, 7, 8}.

(i) Let E₁ be the event of getting 8, then

E₁ = {8}.

∴ The number of favourable outcomes to the event E₁ = 1.

$\therefore P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{1}{8}.

Hence, the probability of getting 8 is $\dfrac{1}{8}$.

(ii) Let E₂ be the event of getting an odd number, then

E₂ = {1, 3, 5, 7}.

∴ The number of favourable outcomes to the event E₂ = 4.

$\therefore P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{4}{8} = \dfrac{1}{2}.

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

(iii) Let E₃ be the event of getting a number greater than 2, then

E₃ = {3, 4, 5, 6, 7, 8}.

∴ The number of favourable outcomes to the event E₃ = 6.

$\therefore P(E$3) = \dfrac{\text{No. of favourable outcomes to } E3}{\text{Total no. of possible outcomes}} = \dfrac{6}{8} = \dfrac{3}{4}.

Hence, the probability of getting a number greater than 2 is $\dfrac{3}{4}$.

(iv) Let E₄ be the event of getting a number less than 9, then

E₄ = {1, 2, 3, 4, 5, 6, 7, 8}.

∴ The number of favourable outcomes to the event E₄ = 8.

$\therefore P(E$4) = \dfrac{\text{No. of favourable outcomes to } E4}{\text{Total no. of possible outcomes}} = \dfrac{8}{8} = 1.

Hence, the probability of of getting a number less than 9 is 1.