Question

Question 3
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, determine the number of blue balls in the bag.

Answer 1

Let there be x blue balls in the bag.
So, the total number of balls in the bag = 5 + x
Now, the probability of drawing a blue ball
$=\frac{x}{5+x}$
And , the probability of drawing a red ball
$=\frac{5}{5+x}$
But according to question, the probability of drawing a blue ball is double that of a red ball,
$\Rightarrow$ $\frac{x}{5+x}=2\times \frac{5}{5+x}\Rightarrow \frac{x}{5+x}=\frac{10}{5+x}$
$\Rightarrow$ $x^2+5x=50+10x$
$\Rightarrow$ $x^2-5x-50=0$
$\Rightarrow$ $x=\frac{5\pm \sqrt{25+(4\times 5)}}{2}$
$\Rightarrow$ $x=\frac{5\pm 15}{2}$
$\Rightarrow$ x = 10 or -5.
Here, number of blue balls cannot be negative.
$\Rightarrow$ x = 10
Hence, there are 10 blue balls in the bag.