Mathematics

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is four times that of a red ball, find the number of balls in the bag.

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Let no. of blue balls be x, so total no. of balls = x + 5.

Given,

P(a blue ball drawn) = 4 × P(a red ball drawn) .

$\Rightarrow \dfrac{x}{x + 5} = 4 \times \dfrac{5}{x + 5} \\[1em] \Rightarrow \dfrac{x}{x + 5} = \dfrac{20}{x + 5} \\[1em] \Rightarrow x = 20.$

Total no. of balls = x + 5 = 20 + 5 = 25.

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