Question

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 white?

Answer 1

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

Let E₂ = Event of selecting a ball which is white

∴ n(E₂) = Number of white balls = 8

 So, required probability = `(n(E_2))/(n(S)) = 8/24 = 1/3`