Question

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

Answer 1

Let the number of blue balls in the bag be x.
Then, total number of balls = ( 5 + x)
Given: P(a blue ball) = 3 × P(a red ball)
$$\begin{gathered} \therefore \frac{x}{\left(5+x\right)}=3\times \frac{5}{\left(5+x\right)} \\ \Rightarrow x\left(5+x\right)=15\left(5+x\right) \\ \Rightarrow x\left(5+x\right)-15\left(5+x\right)=0 \\ \Rightarrow \left(5+x\right)\left(x-15\right) \\ \mathrm{Either}5+x=0\mathrm{or}x-15=0 \\ \mathrm{So}\mathrm{either}x=-5\mathrm{or}x=15 \\ \mathrm{But}\mathrm{number}\mathrm{of}\mathrm{ball}s\mathrm{cannot}\mathrm{be}\mathrm{negative}. \\ \mathrm{Therefore},x=15 \end{gathered}$$
Hence, the number of blue balls in the bag is 15.