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A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.
Given:
A bag contains 6 red balls and some blue balls. The probability of drawing a blue ball from the bag is twice that of a red ball.
To do:
We have to find the number of blue balls in the bag.
Solution:
Let $P( B)$ and $P( R)$ be the probability of drawing a blue ball and a red ball respectively.
Let the number of blue balls in the bag $=x$
This implies,
Total number of balls in the bag $=6+x$
Probability of drawing a blue ball$=\frac{Number\ of\ blue\ balls}{Total\ number\ of\ balls}$
$P( B)=\frac{x}{6+x}$
Probability of drawing a red ball$=\frac{Number\ of\ red\ balls}{Total\ number\ of\ balls}$
$P( R)=\frac{6}{6+x}$
According to the question,
$P( B)=2P( R)$
$\Rightarrow \frac{x}{6+x}=2( \frac{6}{6+x})$
$\Rightarrow x=12$
Hence, the number of blue balls in the bag is $12$.