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.

Answer 1

Total number of balls = 12

Total number of black balls = x

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

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

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

According to the condition given in the question,

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

3x = x + 6

2x = 6

x = 3