Question:
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.
Solution:
Let the number of blue balls be x.
Number of red balls = 5
Total number of balls = x + 5
$P($ getting a red ball $)=\frac{5}{x+5}$
$\mathrm{P}($ getting a blue ball $)=\frac{x}{x+5}$
Given that,
$2\left(\frac{5}{x+5}\right)=\frac{x}{x+5}$
$10(x+5)=x^{2}+5 x$
$x^{2}-5 x-50=0$
$x^{2}-10 x+5 x-50=0$
$x(x-10)+5(x-10)=0$
$(x-10)(x+5)=0$
Either $x-10=0$ or $x+5=0$
$x=10$ or $x=-5$
However, the number of balls cannot be negative.
Hence, number of blue balls = 10