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Mathematics

A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball is twice that of a red ball, find the number of balls in the bag.

Probability

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Answer

Let no. of blue balls be x, total no. of balls = x + 6.

P(drawing a blue ball) = No. of favourable outcomesTotal outcomes=xx+6\dfrac{\text{No. of favourable outcomes}}{\text{Total outcomes}} = \dfrac{x}{x + 6}

P(drawing a red ball) = No. of favourable outcomesTotal outcomes=6x+6\dfrac{\text{No. of favourable outcomes}}{\text{Total outcomes}} = \dfrac{6}{x + 6}.

Given, P(drawing a blue ball) = 2 × P(drawing a red ball)

∴xx+6=2×6x+6⇒xx+6=12x+6⇒x=12.\therefore \dfrac{x}{x + 6} = 2 \times \dfrac{6}{x + 6} \\[1em] \Rightarrow \dfrac{x}{x + 6} = \dfrac{12}{x + 6} \\[1em] \Rightarrow x = 12.

Total no. of balls = x + 6 = 12 + 6 = 18.

Hence, there are 18 balls in the bag.

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