Question

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

Answer 1

Step 1 : The content we have and the formula for the probability

Number of red balls $=5$

Number of blue balls $=x$

$P\left(A\right)=\frac{\text{number of outcome favourable to A}}{\text{total number of possible outcome}}$

or

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

where,

• $P\left(A\right)$ is probability of an event $\text{'}A\text{'}$
• $n\left(A\right)$ is the favorable outcome of the event $\text{'}A\text{'}$
• $n\left(S\right)$ is total number of possible outcome in a sample space

Step 2: Probability of blue and red balls

Let $\left(A\right)$ be the event of getting blue balls, $n\left(A\right)$ and $n\left(S\right)$ be the number of blue balls and total balls available accordingly.

$\left(B\right)$ be the event of getting red balls, $n\left(B\right)$ and $n\left(S\right)$ be the number of red balls and total balls available accordingly.

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$

$\text{Total number of balls}=5+x$

$P\left(A\right)=\frac{x}{5+x}$

$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}$

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

Step 3: Applying the condition

Probability of drawing blue ball according to the condition$=2\times P\left(B\right)$

$\frac{x}{5+x}=2\left[\frac{5}{5+x}\right]$

$x=2\times 5=10$

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