Mathematics

A bag contains 24 balls of which x are red, 2x are white and 3x are blue. A ball is selected at random. Find the probability that it is
(i) white
(ii) not red.

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Total balls = x + 2x + 3x = 24.

⇒ 6x = 24
⇒ x = 4.

(i) P(drawing a white ball) = $\dfrac{\text{No. of white balls}}{\text{Total balls}} = \dfrac{2 \times 4}{24} = \dfrac{1}{3}.$

Hence, the probability of drawing a white ball is $\dfrac{1}{3}$ .

(ii) Total no. of white and blue balls = 2x + 3x = 5x = 20.

P(A) = P(drawing a not red ball) = P(drawing a white or blue ball).

$\therefore P(A) = \dfrac{\text{Total no. of white and blue balls}}{\text{Total balls}} \\[1em] = \dfrac{20}{24} \\[1em] = \dfrac{5}{6}.$

Hence, the probability of not drawing a red ball is $\dfrac{5}{6}$ .

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