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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.

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.

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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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