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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 not red?
Solution
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 E1 = Event of selecting a ball which is not red i.e., can be white or blue.
∴ n(E1) = Number of white balls + Number of blue balls
⇒ n(E1) = 8 + 12 = 20
∴ Required probability = `(n(E_1))/(n(S)) = 20/24 = 5/6`
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