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

Let no. of blue balls be x.

Total balls = (x + 5).

∴ No. of possible outcomes = x + 5

There are 5 red balls

∴ No. of favourable outcomes for drawing a red ball = 5

P(drawing a red ball) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{5}{5 + x}$.

There are x blue balls

∴ No. of favourable outcomes for drawing a blue ball = x

P(drawing a blue ball) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{x}{5 + x}$.

Given,

Probability of drawing a blue ball is double that of red ball.

$\therefore \dfrac{x}{5 + x} = 2 \times \dfrac{5}{5 + x} \\[1em] \Rightarrow \dfrac{x}{5 + x} = \dfrac{10}{5 + x} \\[1em] \Rightarrow x = 10.$

Hence, no. of blue balls = 10.