Question

A bag contains $3$ red balls and some blue balls. If the probability of drawing a blue ball is thrice that of the red ball, find the number of blue balls in the bag.

Answer 1

Step 1 Finding the number of favorable outcomes and the total number of outcomes:

There are $3$ red balls and $n$ blue balls(assumed) in a bag.

Therefore, the total number of outcomes is $n+3$.

Step 2 Finding the number of blue balls:

The formula for probability is,

$$\begin{gathered} Probablity=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \Rightarrow P\left(red\right)=\frac{3}{n+3} \\ \Rightarrow P\left(blue\right)=\frac{n}{n+3} \end{gathered}$$

As per the question,

$$\begin{gathered} \Rightarrow P\left(blue\right)=3\times P\left(red\right) \\ \Rightarrow \frac{n}{n+3}=3\times \frac{3}{n+3} \\ \Rightarrow n=9 \end{gathered}$$

Henceforth, the number of blue balls is $9$.