# 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 $12$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

235 Views