# A box contains 12 balls out of which x are black.

Question:

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?

If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Solution:

Total number of balls = 12

Total number of black balls = x

$\mathrm{P}($ getting a black ball $)=\frac{x}{12}$

If 6 more black balls are put in the box, then

Total number of balls = 12 + 6 = 18

Total number of black balls = x + 6

$\mathrm{P}($ getting a black ball now $)=\frac{x+6}{18}$

According to the condition given in the question,

$2\left(\frac{x}{12}\right)=\frac{x+6}{18}$

$3 x=x+6$

$2 x=6$

$x=3$