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, then find the number of blue balls in a 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: To find the number of blue balls in a 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 no of balls in bag $=5+x$  [No. of red ball $=5$]

Probability of drawing a blue ball$=\frac{No.\ of\ blue\ ball}{Total\ no\ of\ ball}$

​

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

​

Probability of drawing a Red ball$=\frac{No.\ of\ red\ ball}{Total\ no\ of\ ball}$

​

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

As given,

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

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

$\Rightarrow x=10$

​

Hence, no. of blue balls in the bag $=10$.

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Updated on: 10-Oct-2022

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