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

Given:

A bag contains $5$ red balls and some blue balls. The probability of drawing a blue ball is double 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 red ball respectively.

Let number of blue balls in the bag $=x$

Total number of balls in bag $=5+x$  [Number of red ball $=5$]

Probability of drawing a blue ball$=\frac{Number\ of\ blue\ balls}{Total\ number\ of\ balls}$

$P( B)=\frac{x}{5+x}$

Probability of drawing a Red ball$=\frac{Number\ of\ red\ ball}{Total\ number\ of\ balls}$

$P( R)=\frac{5}{5+x}$

As given,

$P( B)=2P( R)$

$\Rightarrow \frac{x}{5+x}=2( \frac{5}{5+x})$

$\Rightarrow x=10$

Hence, the number of blue balls in the bag is $10$.

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Updated on: 10-Oct-2022

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