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

H Harsh Kankaria

Let there be $x$ number of blue balls in the bag.

Number of red balls = 5

Thus, the total number of balls = total possible outcomes = $5+x$

$P(getting\ a\ red\ ball) = \frac{5}{5+x}$

And, $P(getting\ a\ blue\ ball) = \frac{x}{5+x}$

According to question,

$P(getting\ a\ blue\ ball) = P(getting\ a\ red\ ball)$

$\\ \frac{x}{5+x} = 2.\left (\frac{5}{5+x} \right )$

$\implies x = 2.5 = 10$

Therefore, there are 10 blue balls in the bag.

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