A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is

(i) not red?

(ii) white

Given that, A bag contains total number of balls = 24

A bag contains number of red balls = x

A bag contains number of white balls _{= 2x}

and a bag contains number of blue balls _{= 3x}

By condition, _{x + 2x + 3x = 24}

⇒ 6x = 24

⇒ x = 4

∴ Number of red balls = x = 4

Number of white balls = 2x = 2×4 = 8

and number of blue balls = 3x = 3×4 = 12

So, total number of outcomes for a ball is selected at random in a bag contains 24 balls.

⇒ n(S) = 24

(i) Let E_{1} = Event of selecting a ball which is not red i.e., can be white or blue.

∴ n(E_{1}) =Number of white balls + Number of blue balls

⇒ ∴ n(E_{1}) = 8 + 12 = 20

(ii) Let E_{2} Event of selecting a ball which is white

Number of white ball = 8

So, required probability

42