Question

A bag contains $6$ red balls and some blue balls. If the probability of drawing a blue ball is twice that of drawing a red ball, then find the number of blue balls in the bag.

Answer 1

Let the number of blue balls $=x\therefore$ total number of balls $=(6+x)$
$P_{\left(\text{drawing a red ball}\right)}=\frac{6}{6+x}\therefore P_{\left(\text{drawing a blue ball}\right)}=\left(\frac{x}{6+x}\right)\therefore \frac{x}{6+x}=2\left(\frac{6}{6+x}\right)$

$\therefore \frac{x}{6+x}=\frac{12}{6+x}$

$12(6+x)=x(6+x)\therefore 72+12x=6x+x^2\therefore x^2-6x-72=0$

$\therefore (x-12)(x+6)=0\therefore x=12$

or $x=-6$(not possible)

$\therefore$ The number of blue balls $=12$